Gravitational waves (GWs) have a great potential to probe cosmology. We review early universe sources that can lead to cosmological backgrounds of GWs. We begin by presenting proper definitions of GWs in flat space-time and in a cosmological setting (section 2). Following, we discuss the reasons why early universe GW backgrounds are of a stochastic nature, and describe the general properties of a stochastic background (section 3). We recap current observational constraints on stochastic backgrounds, and discuss the basic characteristics of present and future GW detectors, including advanced LIGO, advanced Virgo, the Einstein telescope, KAGRA, and LISA (section 4). We then review in detail early universe GW generation mechanisms, as well as the properties of the GW backgrounds they give rise to. We classify the backgrounds in five categories: GWs from quantum vacuum fluctuations during standard slow-roll inflation (section 5), GWs from processes that operate within extensions of the standard inflationary paradigm (section 6), GWs from post-inflationary preheating and related non-perturbative phenomena (section 7), GWs from first order phase transitions related or not to the electroweak symmetry breaking (section 8), and GWs from general topological defects, and from cosmic strings in particular (section 9). The phenomenology of these early universe processes is extremely rich, and some of the GW backgrounds they generate can be within the reach of near-future GW detectors. A future detection of any of these backgrounds will provide crucial information on the underlying high energy theory describing the early universe, probing energy scales well beyond the reach of particle accelerators.

http://iopscience.iop.org/article/10.1088/1361-6382/aac608/pdf

Cosmological Backgrounds of Gravitational Waves

We report the first results of the LISA Pathfinder in-flight experiment. The results demonstrate that two free-falling reference test masses, such as those needed for a space-based gravitational wave observatory like LISA, can be put in free fall with a relative acceleration noise with a square root of the power spectral density of 5.2 +/- 0.1 fm s(exp -2)/square root of Hz, or (0.54 +/- 0.01) x 10(exp -15) g/square root of Hz, with g the standard gravity, for frequencies between 0.7 and 20 mHz. This value is lower than the LISA Pathfinder requirement by more than a factor 5 and within a factor 1.25 of the requirement for the LISA mission, and is compatible with Brownian noise from viscous damping due to the residual gas surrounding the test masses. Above 60 mHz the acceleration noise is dominated by interferometer displacement readout noise at a level of (34.8 +/- 0.3) fm square root of Hz, about 2 orders of magnitude better than requirements. At f less than or equal to 0.5 mHz we observe a low-frequency tail that stays below 12 fm s(exp -2)/square root of Hz down to 0.1 mHz. This performance would allow for a space-based gravitational wave observatory with a sensitivity close to what was originally foreseen for LISA.

/pdf/sub-femto-g-free-fall-for-space-based-gravitational-wave-1b27ej2js9.pdf

Sub-Femto-g Free Fall for Space-Based Gravitational Wave Observatories: LISA Pathfinder Results

We investigate the potential for the LISA space-based interferometer to detect the stochastic gravitational wave background produced from different mechanisms during inflation. Focusing on well-motivated scenarios, we study the resulting contributions from particle production during inflation, inflationary spectator fields with varying speed of sound, effective field theories of inflation with specific patterns of symmetry breaking and models leading to the formation of primordial black holes. The projected sensitivities of LISA are used in a model-independent way for various detector designs and configurations. We demonstrate that LISA is able to probe these well-motivated inflationary scenarios beyond the irreducible vacuum tensor modes expected from any inflationary background.

/pdf/science-with-the-space-based-interferometer-lisa-iv-probing-x22adkw9tk.pdf

Science with the space-based interferometer LISA. IV: probing inflation with gravitational waves

According to the weak equivalence principle, all bodies should fall at the same rate in a gravitational field. The MICROSCOPE satellite, launched in April 2016, aims to test its validity at the 10−15 precision level, by measuring the force required to maintain two test masses (of titanium and platinum alloys) exactly in the same orbit.
A nonvanishing result would correspond to a violation of the equivalence principle, or to the discovery of a new long-range force. Analysis of the first data gives δ(Ti; Pt)=[-1+/-9(stat)+/-9(syst)] × 10−15 (1σ statistical uncertainty) for the titanium-platinum Eotvos parameter characterizing the relative difference in their free-fall accelerations.

MICROSCOPE Mission: First Results of a Space Test of the Equivalence Principle.

We review detection methods that are currently in use or have been proposed to search for a stochastic background of gravitational radiation. We consider both Bayesian and frequentist searches using ground-based and space-based laser interferometers, spacecraft Doppler tracking, and pulsar timing arrays; and we allow for anisotropy, non-Gaussianity, and non-standard polarization states. Our focus is on relevant data analysis issues, and not on the particular astrophysical or early Universe sources that might give rise to such backgrounds. We provide a unified treatment of these searches at the level of detector response functions, detection sensitivity curves, and, more generally, at the level of the likelihood function, since the choice of signal and noise models and prior probability distributions are actually what define the search. Pedagogical examples are given whenever possible to compare and contrast different approaches. We have tried to make the article as self-contained and comprehensive as possible, targeting graduate students and new researchers looking to enter this field.

/pdf/detection-methods-for-stochastic-gravitational-wave-23aliito0n.pdf

Detection methods for stochastic gravitational-wave backgrounds: a unified treatment

We present a new technique for measuring the stray electric field in precision space inertial sensors by modulating the electric charge of a free-falling test mass and measuring the resulting coherent Coulomb force. The free charge of the test mass is controlled by ultraviolet photoemission using a pulsed light source synchronized with an oscillating potential capacitively induced on the test mass. We can modulate the test mass charge sinusoidally at an arbitrarily chosen frequency by varying the phase of the UV light pulses relative to the induced test mass potential at the appropriate rate. This technique allows us to optimize the precision of the measurement by choosing a modulation frequency that is within the most sensitive band of the sensor. We present an experimental validation of this approach using an inertial sensor integrated with a torsion pendulum, measuring the equivalent stray potential of the sensor with milliVolt precision in ${10}^{4}\text{ }\text{ }\mathrm{s}$. We discuss the applicability of this technique for the upcoming Laser Interferometer Space Antenna (LISA) gravitational-wave observatory. 

Measurement of stray electric fields in a capacitive inertial sensor using contactless test-mass charge modulation

This paper reports on the methods and results of a theoretical analysis to design an insulator which must provide a thermally quiet environment to test on ground delicate temperature sensors and associated electronics These will fly on board ESA's LISA PathFinder (LPF) mission as part of the thermal diagnostics subsystem of the LISA Test-flight Package (LTP) We evaluate the heat transfer function (in frequency domain) of a central body of good thermal conductivity surrounded by a layer of a very poorly conducting substrate This is applied to assess the materials and dimensions necessary to meet temperature stability requirements in the metal core, where sensors will be implanted for test The analysis is extended to evaluate the losses caused by heat leakage through connecting wires, linking the sensors with the electronics in a box outside the insulator The results indicate that, in spite of the very demanding stability conditions, a sphere of outer diameter of the order one metre is sufficient

Theoretical foundations for on-ground tests of LISA PathFinder thermal diagnostics

High-resolution temperature measurements are required in the LTP, i.e., 10 uK/sqrt(Hz) from 1 mHz to 30 mHz. This has been already accomplished with thermistors and a suitable low noise electronics. However, the frequency range of interest for LISA goes down to 0.1 mHz. Investigations on the performance of temperature sensors and the associated electronics at frequencies around 0.1 mHz have been performed. Theoretical limits of the temperature measurement system and the practical on-ground limitations to test them are shown demonstrating that 1/f noise is not observed in thermistors even at frequencies around 0.1 mHz and amplitude levels of 10 uK/sqrt(Hz).

Extension of the LTP temperature diagnostics to the LISA band: first results

In this paper, we present the design and performance of the upgraded University of Florida torsion pendulum facility for testing inertial sensor technology related to space-based gravitational wave observatories and geodesy missions. In particular, much work has been conducted on inertial sensor technology related to the Laser Interferometer Space Antenna (LISA) space gravitational wave observatory mission. A significant upgrade to the facility was the incorporation of a newly designed and fabricated LISA-like gravitational reference sensor (GRS) based on the LISA Pathfinder GRS. Its LISA-like geometry has allowed us to make noise measurements that are more representative of those in LISA and has allowed for the characterization of the mechanisms of noise induced on a LISA GRS and their underlying physics. Noise performance results and experiments exploring the effect of temperature gradients across the sensor will also be discussed. The LISA-like sensor also includes unique UV light injection geometries for UV LED based charge management. Pulsed and DC charge management experiments have been conducted using the University of Florida charge management group's technology readiness level 4 charge management device. These experiments have allowed for the testing of charge management system hardware and techniques as well as characterizations of the dynamics of GRS test mass charging. The work presented here demonstrates the upgraded torsion pendulum's ability to act as an effective testbed for GRS technology.

https://pubs.aip.org/aip/rsi/article-pdf/doi/10.1063/5.0135125/17797117/054502_1_5.0135125.pdf

Design and performance characterization of a new LISA-like (laser interferometer space antenna-like) gravitational reference sensor and torsion pendulum testbed.

High-sensitivity uniaxial opto-mechanical accelerometers provide very accurate linear acceleration measurements. In addition, an array of at least six accelerometers allows the estimation of linear and angular accelerations and becomes a gyro-free inertial navigation system. In this paper, we analyze the performance of such systems considering opto-mechanical accelerometers with different sensitivities and bandwidths. In the six-accelerometer configuration adopted here, the angular acceleration is estimated using a linear combination of accelerometers’ read-outs. The linear acceleration is estimated similarly but requires a correcting term that includes angular velocities. Accelerometers’ colored noise from experimental data is used to derive, analytically and through simulations, the performance of the inertial sensor. Results for six accelerometers, separated by 0.5 m in a cube configuration show noise levels of 10−7 m s−2 and 10−5 m s−2 (in Allan deviation) for time scales of one second for the low-frequency (Hz) and high-frequency (kHz) opto-mechanical accelerometers, respectively. The Allan deviation for the angular velocity at one second is 10−5 rad s−1 and 5×10−4 rad s−1. Compared to other technologies such as MEMS-based inertial sensors and optical gyroscopes, the high-frequency opto-mechanical accelerometer exhibits better performance than tactical-grade MEMS for time scales shorter than 10 s. For angular velocity, it is only superior for time scales less than a few seconds. The linear acceleration of the low-frequency accelerometer outperforms the MEMS for time scales up to 300 s and for angular velocity only for a few seconds. Fiber optical gyroscopes are orders of magnitude better than the high- and low-frequency accelerometers in gyro-free configurations. However, when considering the theoretical thermal noise limit of the low-frequency opto-mechanical accelerometer, 5×10−11 m s−2, linear acceleration noise is orders of magnitude lower than MEMS navigation systems. Angular velocity precision is around 10−10 rad s−1 at one second and 5×10−7 rad s−1 at one hour, which is comparable to fiber optical gyroscopes. While experimental validation is yet not available, the results shown here indicate the potential of opto-mechanical accelerometers as gyro-free inertial navigation sensors, provided the fundamental noise limit of the accelerometer is reached, and technical limitations such as misalignments and initial conditions errors are well controlled.

/pdf/gyro-free-inertial-navigation-systems-based-on-linear-opto-3rzf8l20.pdf

J Sanjuán

Papers

Measurement of stray electric fields in a capacitive inertial sensor using contactless test-mass charge modulation

Theoretical foundations for on-ground tests of LISA PathFinder thermal diagnostics

Extension of the LTP temperature diagnostics to the LISA band: first results

Design and performance characterization of a new LISA-like (laser interferometer space antenna-like) gravitational reference sensor and torsion pendulum testbed.

Gyro-Free Inertial Navigation Systems Based on Linear Opto-Mechanical Accelerometers