The treatment of first-order phase transitions for standard grand unified theories is shown to break down for models with radiatively induced spontaneous symmetry breaking. It is argued that proper analysis of these transitions which would take place in the early history of the universe can lead to an explanation of the cosmological homogeneity, flatness, and monopole puzzles.

Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking

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Inferring the dark matter power spectrum from the Lyman-Alpha forest in high-resulotion QSO absorption spectra

The cosmic expansion history tests the dynamics of the global evolution of the universe and its energy density contents, while the cosmic growth history tests the evolution of the inhomogeneous part of the energy density Precision comparison of the two histories can distinguish the nature of the physics responsible for the accelerating cosmic expansion: an additional smooth component - dark energy - or a modification of the gravitational field equations With the aid of a new fitting formula for linear perturbation growth accurate to 005-02percent, we separate out the growth dependence on the expansion history and introduce a new growth index parameter \gamma that quantifies the gravitational modification

Cosmic Growth History and Expansion History

Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter H(z) and cosmic microwave background constraints are described with different cosmological models. We compare the ΛCDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale rs(zd). Among the considered models the best value of χ2 is achieved for the model with quadratic equation of state, but it has 2 additional parameters in comparison with the ΛCDM and therefore is not favored by the Akaike information criterion.

https://iopscience.iop.org/article/10.1088/1475-7516/2016/06/023/pdf

Observational constraints on cosmological models with Chaplygin gas and quadratic equation of state

Observational manifestations of accelerated expansion of the universe, in particular, recent data for Type Ia supernovae, baryon acoustic oscillations, for the Hubble parameter $H(z)$ and cosmic microwave background constraints are described with different cosmological models. We compare the $\Lambda$CDM, the models with generalized and modified Chaplygin gas and the model with quadratic equation of state. For these models we estimate optimal model parameters and their permissible errors with different approaches to calculation of sound horizon scale $r_s(z_d)$. Among the considered models the best value of $\chi^2$ is achieved for the model with quadratic equation of state, but it has 2 additional parameters in comparison with the $\Lambda$CDM and therefore is not favored by the Akaike information criterion.

We study cosmological models with modified Chaplygin gas (MCG) to determine observational constraints on its EoS parameters using the background and the growth tests data. The background test data consists of $H(z)-z$
 data, Baryonic Acoustic Oscillations peak parameter, CMB shift parameter, SN Ia data and the growth test data consists of the linear growth function for the large scale structures of the universe are considered to study MCG in favor of dark energy. For a given range of redshift, the Wiggle-Z measurements and rms mass fluctuations from Ly-
 $\alpha $
 data, employed for analyzing cosmological models numerically to constrain the MCG parameters. The Wang-Steinhardt ansatz for the growth index (
 $\gamma $
 ) and growth function (
 $f$
 ) are also considered for numerical analysis. The best-fit values of EoS parameters determined here are used to study the variation of $f$
 , growth index (
 $\gamma $
 ), EoS parameter, squared sound speed and deceleration parameter with redshift. The constraints on the MCG parameters found here are compared with that of GCG (generalized Chaplygin gas) model for viable cosmology. Cosmologies with MCG satisfactorily describe late acceleration followed by a matter dominated phase. The range of values of EoS parameters, the associated parameters (
 $f$
 , $\gamma $
 , $\omega $
 , $\varOmega $
 , $c^{2}_{s}$
 , $q$
 ) are also determined from observational data in order to understand the suitability of the MCG model.

Constraints on modified Chaplygin gas from large scale structure

We investigate emergent universe model using recent observational data for the background tests as well as for the growth tests. The background test data comprises of Hubble data, Baryon Acoustic Oscillation (BAO) data, cosmic microwave background (CMB) shift data, Union compilation data. The observational growth data are obtained from Wiggle-Z measurements and rms mass fluctuations data from Lyman-$\alpha$ measurements at different red shifts. The flat emergent universe model obtained by Mukherjee {\it et. al.} is permitted with a non-linear equation of state (in short, EoS) ($p=A\rho-B\rho^{\frac{1}{2}}$), where $A$ and $B$ are constants. The observed cosmological data are used here to estimate the range of allowed values of EoS parameters numerically. The best-fit values of the EoS and growth parameters are determined making use of chi-square minimization technique. The analysis is carried out here considering the Wang-Steinhardt ansatz for growth index ($\gamma$) and growth function ($f$ defined as $f=\Omega_{m}^{\gamma} (a)$). Subsequently, the best-fit values of the EoS parameters are used to study the evolution of the growth function $f$, growth index $\gamma$, state parameter $\omega$ with red shift parameter $z$. The present value of the parameters, namely, $f$, $\gamma$, $\omega$, $\Omega_{m}$ are also estimated. The late accelerating phase of the universe in the model is accommodated satisfactorily.

Observational Constraints on EoS parameters of Emergent Universe

We investigate emergent universe model using recent observational data of the background as well as the growth tests. The flat emergent universe model obtained by Mukherjee et al. is permitted with a non-linear equation of state (in short, EoS) (
 $p=A\rho -B \rho^{\frac{1}{2}}$
 ), where $A$
 and $B$
 are constants (here in our analysis $A=0$
 is considered). We carried out analysis considering the Wang–Steinhardt ansatz for growth index (
 $\gamma $
 ) and growth function (
 $f$
 defined as $f=\varOmega_{m}^{\gamma } (a)$
 ). The best-fit values of the EoS and growth parameters are determined making use of $chi$
 -square minimization technique. Here we specifically determined the best-fit value and the range of value of the present matter density (
 $\varOmega _{m}$
 ) and Hubble parameter (
 $H_{0}$
 ). The best-fit values of the EoS parameters are used to study the evolution of the growth function $f$
 , growth index $\gamma $
 , state parameter $\omega $
 and deceleration parameter (
 $q$
 ) for different red shift parameter $z$
 . The late accelerating phase of the universe in the EU model is accommodated satisfactorily.

We study cosmological models with modified Chaplygin gas (in short, MCG) to determine observational constraints on its EoS parameters. The observational data of the background and the growth tests are employed. The background test data namely, H(z)-z data, CMB shift parameter, Baryonic acoustic oscillations (BAO) peak parameter, SN Ia data are considered to study the dynamical aspects of the universe. The growth test data we employ here consists of the linear growth function for the large scale structures of the universe, models are explored assuming MCG as a candidate for dark energy. Considering the observational growth data for a given range of redshift from the Wiggle-Z measurements and rms mass fluctuations from Ly-$\alpha$ measurements, cosmological models are analyzed numerically to determine constraints on the MCG parameters. In this case, the Wang-Steinhardt ansatz for the growth index $\gamma$ and growth function $f$ (defined as $f=\Omega_{m}^{\gamma} (a)$) are also taken into account for the numerical analysis. The best-fit values of the equation of state parameters obtained here are used to study the variation of the growth function ($f$), growth index ($\gamma$), equation of state parameter ($\omega$), squared sound speed $c^2_{s}$ and deceleration parameter with redshift. The observational constraints on the MCG parameters obtained here are then compared with those of the GCG model for viable cosmology. It is noted that MCG models satisfactorily accommodate an accelerating phase followed by a matter dominated phase of the universe. The permitted range of values of the EoS parameters and the associated parameters ($f$, $\gamma$, $\omega$, $\Omega$, $c^2_{s}$, $q$) are compared with those obtained earlier using other observations.

Prasenjit Thakur

Papers

Constraints on modified Chaplygin gas from large scale structure

Observational Constraints on EoS parameters of Emergent Universe

Observational Constraints on EoS parameters of Emergent Universe

Observational constraints on Modified Chaplygin Gas from Large Scale Structure