Showing papers on "Particle horizon published in 2009"

The Primordial Density Perturbation: Cosmology, Inflation and the Origin of Structure

Abstract: The origin and evolution of the primordial perturbation is the key to understanding structure formation in the earliest stages of the Universe It carries clues to the types of physical phenomena active in that extreme high-density environment Through its evolution, generating first the observed cosmic microwave background anisotropies and later the distribution of galaxies and dark matter in the Universe, it probes the properties and dynamics of the present Universe This graduate-level textbook gives a thorough account of theoretical cosmology and perturbations in the early Universe, describing their observational consequences and showing how to relate such observations to primordial physical processes, particularly cosmological inflation With ambitious observational programmes complementing ever-increasing sophistication in theoretical modelling, cosmological studies will remain at the cutting edge of astrophysical studies for the foreseeable future

An upper limit on the stochastic gravitational-wave background of cosmological origin

Abstract: A stochastic background of gravitational waves is expected to arise from a superposition of a large number of unresolved gravitational-wave sources of astrophysical and cosmological origin. It should carry unique signatures from the earliest epochs in the evolution of the Universe, inaccessible to standard astrophysical observations. Direct measurements of the amplitude of this background are therefore of fundamental importance for understanding the evolution of the Universe when it was younger than one minute. Here we report limits on the amplitude of the stochastic gravitational-wave background using the data from a two-year science run of the Laser Interferometer Gravitational-wave Observatory (LIGO). Our result constrains the energy density of the stochastic gravitational-wave background normalized by the critical energy density of the Universe, in the frequency band around 100 Hz, to be <6.9 times 10-6 at 95% confidence. The data rule out models of early Universe evolution with relatively large equation-of-state parameter, as well as cosmic (super)string models with relatively small string tension that are favoured in some string theory models. This search for the stochastic background improves on the indirect limits from Big Bang nucleosynthesis and cosmic microwave background at 100 Hz.

Hawking radiation of an apparent horizon in a FRW universe

Abstract: Hawking radiation is an important quantum phenomenon of a black hole, which is closely related to the existence of an event horizon of a black hole. The cosmological event horizon of de Sitter space is also of Hawking radiation with a thermal spectrum. By use of the tunneling approach, we show that there is indeed a Hawking radiation with temperature, T = 1/2 pi(r) over tilde (A), for a locally defined apparent horizon of a Friedmann-Robertson-Walker universe with any spatial curvature, where (r) over tilde (A) is the apparent horizon radius. Thus we fill in the gap existing in the literature investigating the relation between the first law of thermodynamics and Friedmann equations; there the apparent horizon is assumed to have such a temperature without any proof. In addition, we stress the implication of the Hawking temperature associated with the apparent horizon.

Archipelagian Cosmology: Dynamics and Observables in a Universe with Discretized Matter Content

Abstract: We consider a model of the Universe in which the matter content is in the form of discrete islands, rather than a continuous fluid In the appropriate limits the resulting large-scale dynamics approach those of a Friedmann-Robertson-Walker (FRW) universe The optical properties of such a space-time, however, do not This illustrates the fact that the optical and "average" dynamical properties of a relativistic universe are not equivalent, and do not specify each other uniquely We find the angular diameter distance, luminosity distance, and redshifts that would be measured by observers in these space-times, using both analytic approximations and numerical simulations While different from their counterparts in FRW, the effects found do not look like promising candidates to explain the observations usually attributed to the existence of dark energy This incongruity with standard FRW cosmology is not due to the existence of any unexpectedly large structures or voids in the Universe, but only to the fact that the matter content of the Universe is not a continuous fluid

Can a matter-dominated model with constant bulk viscosity drive the accelerated expansion of the universe?

Abstract: We test a cosmological model which the only component is a pressureless fluid with a constant bulk viscosity as an explanation for the present accelerated expansion of the universe. We classify all the possible scenarios for the universe predicted by the model according to their past, present and future evolution and we test its viability performing a Bayesian statistical analysis using the SCP ``Union'' data set (307 SNe Ia), imposing the second law of thermodynamics on the dimensionless constant bulk viscous coefficient and comparing the predicted age of the universe by the model with the constraints coming from the oldest globular clusters. The best estimated values found for and the Hubble constant H0 are: = 1.922±0.089 and H0 = 69.62±0.59 (km/s)Mpc−1 with a χ2min = 314 (χ2d.o.f = 1.031). The age of the universe is found to be 14.95±0.42 Gyr. We see that the estimated value of H0 as well as of χ2d.o.f are very similar to those obtained from ΛCDM model using the same SNe Ia data set. The estimated age of the universe is in agreement with the constraints coming from the oldest globular clusters. Moreover, the estimated value of is positive in agreement with the second law of thermodynamics (SLT). On the other hand, we perform different forms of marginalization over the parameter H0 in order to study the sensibility of the results to the way how H0 is marginalized. We found that it is almost negligible the dependence between the best estimated values of the free parameters of this model and the way how H0 is marginalized in the present work. Therefore, this simple model might be a viable candidate to explain the present acceleration in the expansion of the universe.

Signals From the Epoch of Cosmological Recombination

Abstract: The physical ingredients to describe the epoch of cosmological recombination are amazingly simple and well-understood. This fact allows us to take into account a very large variety of physical processes, still finding potentially measurable consequences for the energy spectrum and temperature anisotropies of the Cosmic Microwave Background (CMB). In this contribution we provide a short historical overview in connection with the cosmological recombination epoch and its connection to the CMB. Also we highlight some of the detailed physics that were studied over the past few years in the context of the cosmological recombination of hydrogen and helium. (abrigded)

How flat can you get? A model comparison perspective on the curvature of the Universe

Abstract: The question of determining the spatial geometry of the Universe is of greater relevance than ever, as precision cosmology promises to verify inflationary predictions about the curvature of the Universe. We revisit the question of what can be learnt about the spatial geometry of the Universe from the perspective of a three-way Bayesian model comparison. By considering two classes of phenomenological priors for the curvature parameter, we show that, given the current data, the probability that the Universe is spatially infinite lies between 67 and 98 per cent, depending on the choice of priors. For the strongest prior choice, we find odds of the order of 50:1 (200:1 ) in favour of a flat Universe when compared with a closed (open) model. We also report a robust, prior-independent lower limit to the number of Hubble spheres in the Universe, N U ≥ 5 (at 99 per cent confidence). We forecast the accuracy with which future cosmic microwave background (CMB) and baryonic acoustic oscillation (BAO) observations will be able to constrain curvature, finding that a cosmic variance-limited CMB experiment together with an Square Kilometer Array (SKA)-like BAO observation will constrain curvature independently of the equation of state of dark energy with a precision of about σ ∼ 4.5 x 10 ―4 . We demonstrate that the risk of 'model confusion' (i.e. wrongly favouring a flat Universe in the presence of curvature) is much larger than might be assumed from parameter error forecasts for future probes. We argue that a 5σ detection threshold guarantees a confusion- and ambiguity-free model selection. Together with inflationary arguments, this implies that the geometry of the Universe is not knowable if the value of the curvature parameter is below |Ω κ | ∼ 10- 4 . This bound is one order of magnitude larger than what one would naively expect from the size of curvature perturbations, ∼10 ―5 .

Phenomenological model for the early universe

Abstract: We consider the description of cosmological dynamics from the onset of inflation by a perfect fluid whose parameters must be consistent with the strength of the enhanced quantum loop effects that can arise during inflation. The source of these effects must be nonlocal and a simple incarnation of it is studied both analytically and numerically. The resulting evolution stops inflation in a calculable amount of time and leads to an oscillatory universe with a vanishing mean value for the curvature scalar and an oscillation frequency which we compute.

Model independent constraints on the cosmological expansion rate

Abstract: We investigate what current cosmological data tells us about the cosmological expansion rate in a model independent way. Specifically, we study if the expansion was decelerating at high redshifts and is accelerating now, without referring to any model for the energy content of the universe, nor to any specific theory of gravity. This differs from most studies of the expansion rate which, e.g., assumes some underlying parameterised model for the dark energy component of the universe. To accomplish this, we have devised a new method to probe the expansion rate without relying on such assumptions. Using only supernova data, we conclude that there is little doubt that the universe has been accelerating at late times. However, contrary to some previous claims, we can not determine if the universe was previously decelerating. For a variety of methods used for constraining the expansion history of the universe, acceleration is detected from supernovae alone at >5σ, regardless of the curvature of the universe. Specifically, using a Taylor expansion of the scale factor, acceleration today is detected at >12σ. If we also include the ratio of the scale of the baryon acoustic oscillations as imprinted in the cosmic microwave background and in the large scale distribution of galaxies, it is evident from the data that the expansion decelerated at high redshifts, but only with the assumption of a flat or negatively curved universe.

Dark energy and the return of the phoenix universe

Abstract: In cyclic universe models based on a single scalar field (e.g., the radion determining the distance between branes in M theory), virtually the entire Universe makes it through the ekpyrotic smoothing and flattening phase, bounces, and enters a new epoch of expansion and cooling. This stable evolution cannot occur, however, if scale-invariant curvature perturbations are produced by the entropic mechanism because it requires two scalar fields (e.g., the radion and the Calabi-Yau dilaton) evolving along an unstable classical trajectory. In fact, we show here that an overwhelming fraction of the Universe fails to make it through the ekpyrotic phase; nevertheless, a sufficient volume survives and cycling continues forever provided the dark energy phase of the cycle lasts long enough, of order a trillion years. Two consequences are a new role for dark energy and a global structure of the Universe radically different from that of eternal inflation.

Is the Universe Rotating

Abstract: Models of a rotating universe have been studied widely since the work of G?del, who showed an example that is consistent with general relativity. By now, the possibility of a rotating universe has been discussed comprehensively in the framework of some types of Bianchi's models, such as Type V, VII, and IX and different approaches have been proposed to constrain the rotation. Recent discoveries of some non-Gaussian properties of the Cosmic Microwave Background Anisotropies (CMBA), such as the suppression of the quadrupole and the alignment of some multipoles draw attention to some Bianchi models with rotation. However, cosmological data, such as those of the CMBA, strongly prefer a homogeneous and isotropic model. Therefore, it is of interest to discuss the rotation of the universe as a perturbation of the Robertson-Walker metric, to constrain the rotating speed by cosmological data and to discuss whether it could be the origin of the non-Gaussian properties of the CMBA mentioned above. Here, we derive the general form of the metric (up to second-order perturbations) which is compatible with the rotation perturbation in a flat ?-CDM universe. By comparing the second-order Sachs-Wolfe effect due to rotation with the CMBA data, we constrain the angular speed of the rotation to be less than 10?9 rad?yr?1 at the last scattering surface. This provides the first constraint on the shear-free rotation of a ?CDM universe.

Relation between the isotropy of the CMB and the geometry of the universe

Abstract: The near isotropy of the cosmic microwave background (CMB) is considered to be the strongest indication for the homogeneity and isotropy of the Universe, a cornerstone of most cosmological analysis. We derive new theorems which extend the Ehlers-Geren-Sachs result that an isotropic CMB implies that the Universe is either stationary or homogeneous and isotropic, and its generalization to the almost isotropic case. We discuss why the theorems do not apply to the real Universe, and why the CMB observations do not imply that the Universe would be nearly homogeneous and isotropic.

Large-Scale Structure of the Universe as a Cosmic Standard Ruler

Abstract: We propose to use the large-scale structure of the universe as a cosmic standard ruler, based on the fact that the pattern of galaxy distribution should be maintained in the course of time on large scales. By examining the scale-dependence of the pattern in different redshift intervals it is possible to reconstruct the expansion history of the universe, and thus to measure the cosmological parameters governing the expansion of the universe. The features in the galaxy distribution that can be used as standard rulers include the topology of large-scale structure and the overall shapes of galaxy power spectrum and correlation function. The genus, being an intrinsic topology measure, is resistant against the non-linear gravitational evolution, galaxy biasing, and redshift-space distortion effects, and thus is ideal for quantifying the primordial topology of the large-scale structure. The expansion history of the universe can be constrained by comparing among the genus measured at different redshifts. In the case of initially Gaussian fluctuations the genus accurately recovers the slope of the primordial power spectrum near the smoothing scale, and the expansion history can be constrained by comparing between the predicted and measured genus.

Model- and calibration-independent test of cosmic acceleration

Abstract: We present a calibration-independent test of the accelerated expansion of the universe using supernova type Ia data. The test is also model-independent in the sense that no assumptions about the content of the universe or about the parameterization of the deceleration parameter are made and that it does not assume any dynamical equations of motion. Yet, the test assumes the universe and the distribution of supernovae to be statistically homogeneous and isotropic. A significant reduction of systematic effects, as compared to our previous, calibration-dependent test, is achieved. Accelerated expansion is detected at significant level (4.3σ in the 2007 Gold sample, 7.2σ in the 2008 Union sample) if the universe is spatially flat. This result depends, however, crucially on supernovae with a redshift smaller than 0.1, for which the assumption of statistical isotropy and homogeneity is less well established.

On the Stability of Jordan-Brans-Dicke Static Universe

Abstract: In this work we study the stability of the Jordan-Brans-Dicke (JBD) static universe. This is motivated by the possibility that the universe might have started out in an asymptotically JBD static state, in the context of the so called emergent universe scenario. We extent our previous results on stability of JBD static universe by considering spatially homogeneous Bianchi type IX anisotropic perturbation modes and by including more general perfect fluids. Contrary to general relativity, we have found that the JBD static universe, dominated by a standard perfect fluid, could be stable against isotropic and anisotropic perturbations. The implications of these results for the initial state of the universe and its pre-inflationary evolution are discussed.

The evolution of our local cosmic domain: effective causal limits

Abstract: The causal limit usually considered in cosmology is the particle horizon, delimiting the possibilities of causal connection in the expanding Universe. However, it is not a realistic indicator of the effective local limits of important interactions in space–time. We consider here the matter horizon for the Solar system, i.e. the comoving region which has significantly contributed matter to our local physical environment. This lies inside the effective domain of dependence, which (assuming the universe is dominated by dark matter along with baryonic matter and vacuum-energy-like dark energy) consists of those regions that have had a significant active physical influence on this environment through effects such as matter accretion and acoustic waves. It is not determined by the velocity of light c, but by the flow of matter perturbations along their world lines and associated gravitational effects. We emphasize how small a region the perturbations which became our Galaxy occupied, relative to the observable universe – even relative to the smallest scale perturbations detectable in the cosmic microwave background radiation. Finally, looking to the future of our local cosmic domain, we suggest simple dynamical criteria for determining the present domain of influence and the future matter horizon. The former is the radial distance at which our local region is just now separating from the cosmic expansion. The latter represents the limits of growth of the matter horizon in the far future.

Planck’s constant variation as a cosmological evolution test for the early universe

Abstract: A conjecture on a hierarchical cosmological time evolution of Planck’s constant has been accepted. This presumed phenomenon might be responsible for the cosmological high redshifts as an alternative mechanism instead of the Doppler effect. The Bohr radius of a hydrogen atom and the probability of alpha decay of atomic nuclei have been estimated: both results are in sufficient consent with observational data concerning the light elements abundance in the early Universe.

Entropy of the Universe

Abstract: After a discussion on several limiting cases where General Relativity turns into less sophisticated theories, we find that in the correct thermodynamical and cosmological weak field limit of Einstein’s field equations the entropy of the Universe is R 3/2-dependent, where R stands for the radius of the causally related Universe. Thus, entropy grows in the Universe, contrary to Standard Cosmology prediction.

Phenomenology of the Invisible Universe

Abstract: Cosmology is operating now on a well established and tightly constraining empirical basis. The relativistic LambdaCDM hot big bang theory is consistent with all the present tests; it has become the benchmark. But the many open issues in this subject make it reasonable to expect that a more accurate cosmology will have more interesting physics in the invisible sector of the universe, and maybe also in the visible part.

Quantum Corrections to the Cosmological Evolution of Conformally Coupled Fields

Abstract: Because the source term for the equations of motion of a conformally coupled scalar field, such as the dilaton, is given by the trace of the matter energy momentum tensor, it is commonly assumed to vanish during the radiation dominated epoch in the early universe. As a consequence, such fields are generally frozen in the early universe. Here we compute the finite temperature radiative correction to the source term and discuss its consequences on the evolution of such fields in the early universe. We discuss in particular, the case of scalar tensor theories of gravity which have general relativity as an attractor solution. We show that, in some cases, the universe can experience an early phase of contraction, followed by a non-singular bounce, and standard expansion. This can have interesting consequences for the abundance of thermal relics; for instance, it can provide a solution to the gravitino problem. We conclude by discussing the possible consequences of the quantum corrections to the evolution of the dilaton.

The residual gravity acceleration effect in the Poincaré dodecahedral space

Abstract: Context. In a flat space, it has been shown heuristically that the global topology of comoving space can affect the dynamics expected in the weak-field Newtonian limit, inducing a weak acceleration effect similar to dark energy.Aims. Does a similar effect occur in the case of the Poincare dodecahedral space, which is a candidate model of comoving space for solving the missing fluctuations problem observed in cosmic microwave background all-sky maps? Moreover, does the effect distinguish the Poincare space from other well-proportioned spaces?Methods. The acceleration effect in the Poincare space is studied, using a massive particle and a nearby test particle of negligible mass. Calculations are made in S 3 embedded in . The weak-limit gravitational attraction on a test particle at distance r is set to be rather than , where is the curvature radius, in order to satisfy Stokes' theorem. A finite particle horizon large enough to include the adjacent topological images of the massive particle is assumed. The regular, flat, 3-torus T 3 is re-examined, and two other well-proportioned spaces, the octahedral space , and the truncated cube space , are also studied.Results. The residual gravity effect occurs in all four cases. In a perfectly regular 3-torus of side length L a , and in the octahedral and truncated cube spaces, the highest order term in the residual acceleration is the third-order term in the Taylor expansion in powers of (3-torus), or , respectively. However, the Poincare dodecahedral space is unique among the four spaces. The third order cancels, leaving the fifth order term as the most significant.Conclusions. Not only are three of the four perfectly regular well-proportioned spaces better balanced than most other multiply connected spaces in terms of the residual gravity acceleration effect by a factor of about a million (setting = ~ 10-3 ), but the fourth of these spaces is about ten thousand times better balanced than the other three. This is the Poincare dodecahedral space. Is this unique dynamical property of the Poincare space a clue towards a theory of cosmic topology?

Warm-Intermediate inflationary universe model

Abstract: Warm inflationary universe models in the context of intermediate expansion, between power law and exponential, are studied. General conditions required for these models to be realizable are derived and discussed. This study is done in the weak and strong dissipative regimes. The inflaton potentials considered in this study are negative-power-law and powers of logarithms, respectively. The parameters of our models are constrained from the WMAP three and five year data.

Non-Gaussianity as a Probe of the Physics of the Primordial Universe and the Astrophysics of the Low Redshift Universe

Abstract: A new and powerful probe of the origin and evolution of structures in the Universe has emerged and been actively developed over the last decade. In the coming decade, non-Gaussianity, i.e., the study of non-Gaussian contributions to the correlations of cosmological fluctuations, will become an important probe of both the early and the late Universe. Specifically, it will play a leading role in furthering our understanding of two fundamental aspects of cosmology and astrophysics: (i) the physics of the very early universe that created the primordial seeds for large-scale structures, and (ii) the subsequent growth of structures via gravitational instability and gas physics at later times. To date, observations of fluctuations in the Cosmic Microwave Background (CMB) and the Large-Scale Structure of the Universe (LSS) have focused largely on the Gaussian contribution as measured by the two-point correlations (or the power spectrum) of density fluctuations. However, an even greater amount of information is contained in non-Gaussianity and a large discovery space therefore still remains to be explored. Many observational probes can be used to measure non-Gaussianity, including CMB, LSS, gravitational lensing, Lyman-alpha forest, 21-cm fluctuations, and the abundance of rare objects such as clusters of galaxies and high-redshift galaxies. Not only does the study of non-Gaussianity maximize the science return from a plethora of present and future cosmological experiments and observations, but it also carries great potential for important discoveries in the coming decade.

A Simple Estimate for the Mass of the Universe: Dimensionless Parameter A and the Construct of "Pressure"

Abstract: Employing a simple model for "pressure", a solution of 10 52 kg for the mass of the Universe was obtained which was identical in orders of magnitude to both empirical estimates and different theoretical solutions derived from more complicated equations. The transforming coefficient was within the error margins of the dimensionless parameter A employed to constrain dark energy models. Application of this mass to Schwarzchild's equation for singularity indicated that about 19% of the universe, now presumed to be dark matter, would meet this criterion. Dimensional analysis requires the mass of the universe to increase as its four-dimensional representation expands.

A New Cosmological Model: Black Hole Universe

Abstract: A new cosmological model called black hole universe is proposed. According to this model, the universe originated from a hot star-like black hole with several solar masses, and gradually grew up through a supermassive black hole with billion solar masses to the present state with hundred billion-trillion solar masses by accreting ambient materials and merging with other black holes. The entire space is structured with infinite layers hierarchically. The innermost three layers are the universe that we are living, the outside called mother universe, and the inside star-like and supermassive black holes called child universes. The outermost layer is infinite in radius and limits to zero for both the mass density and absolute temperature. The relationships among all layers or universes can be connected by the universe family tree. Mathematically, the entire space can be represented as a set of all universes. A black hole universe is a subset of the entire space or a subspace. The child universes are null sets or empty spaces. All layers or universes are governed by the same physics - the Einstein general theory of relativity with the Robertson-walker metric of spacetime - and tend to expand outward physically. The evolution of the space structure is iterative. When one universe expands out, a new similar universe grows up from its inside. The entire life of a universe begins from the birth as a hot star-like or supermassive black hole, passes through the growth and cools down, and expands to the death with infinite large and zero mass density and absolute temperature. The black hole universe model is consistent with the Mach principle, the observations of the universe, and the Einstein general theory of relativity. Its various aspects can be understood with the well-developed physics without any di culty. The dark energy is not required for the universe to accelerate its expansion. The inflation is not necessary because the black hole universe does not exist the horizon problem.

Quantum Tunneling from Apparent Horizon of Rainbow-FRW Universe

Abstract: The quantum tunneling from the apparent horizon of rainbow-FRW universe is studied in this paper. We apply the semi-classical approximation, which is put forward by Parikh and Wilczek et al., to research on the scalar field particles tunneling from the apparent horizon of the rainbow-FRW universe, and then use the spin 1/2 Fermions tunneling theory, which brought forward by Kerner and Mann firstly, to research on the Fermions Hawking radiation via semi-classical approximation. Finally, we discuss the meanings of the quantum effect via Finsler geometry.

Accelerating universe from warped extra dimensions

Abstract: Accelerating universe or the existence of a small and positive cosmological constant is probably the most pressing obstacle as well as opportunity to significantly improving the models of four-dimensional cosmology from fundamental theories of gravity, including string theory. In seeking to resolve this problem, one naturally wonders if the real world can somehow be interpreted as an inflating de Sitter brane embedded in a higher-dimensional spacetime described by warped geometry. In this scenario, the four-dimensional cosmological constant may be uniquely determined in terms of two length scales: one is a scale associated with the size of extra dimensions and the other is a scale associated with the expansion rate of our universe. In some specific cases, these two scales are complementary to each other. This result is demonstrated here by presenting some explicit and completely non-singular de Sitter space dS$_4$ solutions of vacuum Einstein equations in five and ten dimensions.

Causality and Primordial Tensor Modes

Abstract: We introduce the real space correlation function of $B$-mode polarization of the cosmic microwave background (CMB) as a probe of superhorizon tensor perturbations created by inflation. By causality, any non-inflationary mechanism for gravitational wave production after reheating, like global phase transitions or cosmic strings, must have vanishing correlations for angular separations greater than the angle subtended by the particle horizon at recombination, i.e. $\theta \gtrsim 2^\circ$. Since ordinary $B$-modes are defined non-locally in terms of the Stokes parameters $Q$ and $U$ and therefore don't have to respect causality, special care is taken to define `causal $\tilde B$-modes' for the analysis. We compute the real space $\tilde B$-mode correlation function for inflation and discuss its detectability on superhorizon scales where it provides an unambiguous test of inflationary gravitational waves. The correct identification of inflationary tensor modes is crucial since it relates directly to the energy scale of inflation. Wrongly associating tensor modes from causal seeds with inflation would imply an incorrect inference of the energy scale of inflation. We find that the superhorizon $\tilde B$-mode signal is above cosmic variance for the angular range $2^\circ < \theta < 4^\circ$ and is therefore in principle detectable. In practice, the signal will be challenging to measure since it requires accurately resolving the recombination peak of the $B$-mode power spectrum. However, a future CMB satellite (CMBPol), with noise level $\Delta_P \simeq 1\mu$K-arcmin and sufficient resolution to efficiently correct for lensing-induced $B$-modes, should be able to detect the signal at more than 3$\sigma$ if the tensor-to-scalar ratio isn't smaller than $r \simeq 0.01$.

Causality and Primordial Tensor Modes

Abstract: We introduce the real space correlation function of B-mode polarization of the cosmic microwave background (CMB) as a probe of superhorizon tensor perturbations created by inflation. By causality, any non-inflationary mechanism for gravitational wave production after reheating, like global phase transitions or cosmic strings, must have vanishing correlations for angular separations greater than the angle subtended by the particle horizon at recombination, i.e. θ 2°. Since ordinary B-modes are defined non-locally in terms of the Stokes parameters Q and U and therefore don't have to respect causality, special care is taken to define `causal -modes' for the analysis. We compute the real space -mode correlation function for inflation and discuss its detectability on superhorizon scales where it provides an unambiguous test of inflationary gravitational waves. The correct identification of inflationary tensor modes is crucial since it relates directly to the energy scale of inflation. Wrongly associating tensor modes from causal seeds with inflation would imply an incorrect inference of the energy scale of inflation. We find that the superhorizon -mode signal is above cosmic variance for the angular range 2° < θ < 4° and is therefore in principle detectable. In practice, the signal will be challenging to measure since it requires accurately resolving the recombination peak of the B-mode power spectrum. However, a future CMB satellite (CMBPol), with noise level ΔP 1μK-arcmin and sufficient resolution to efficiently correct for lensing-induced B-modes, should be able to detect the signal at more than 3σ if the tensor-to-scalar ratio isn't smaller than r 0.01.