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

Temperature sensors and heaters belong in the diagnostics subsystem of the LISA Technology Package (LTP) on board LISA Pathfinder, the technology demonstrator for LISA. A number of these diagnostics items are placed at short distances from the LTP proof masses, and are negative temperature coefficient (NTC) thermistors. By design, these devices have tiny amounts of ferromagnetic materials which therefore constitute a potential source of disturbance to the performance of the LTP. We present a detailed magnetic characterisation of the NTC's, and use the data to evaluate their impact on the acceleration noise budget of the LTP. The effect is seen to be small, and can be further reduced if the NTC's are submitted to a demagnetisation process before they are attached. Re-magnetisation is unlikely, as rather strong fields (mili-Tesla) are required to re-magnetise the NTC's

Magnetic polarisation effects of temperature sensors and heaters in LISA Pathfinder

The LIGO-Virgo-Kagra (LVK) collaboration has detected gravitational waves from 90 Compact Binary Coalescences. In addition to fortifying the linearized theory of General Relativity (GR), the statistical ensemble of detections also provides prospects of detecting nonlinear effects predicted by GR, one such prediction being the nonlinear gravitational memory effect. For detected stellar and intermediate mass compact binaries, the induced strain from the memory effect is one or two orders below the detector noise background. Additionally, since most of the energy is radiated at merger the strain induced by the memory effect resembles a step function at the merger time. These facts motivate the idea of coherently stacking up data streams from recorded GW events at these merger times so that the cumulative memory strain is detected with a sufficient SNR. GW detectors essentially record the integrated strain response at time scales of the round trip light travel time, making future space-based long arm interferometers like LISA ideal for detecting the memory effect at low frequencies. In this paper, we propose a method that uses the event catalog of ground-based detectors and searches for corresponding memory strains in the LISA data stream. Given LVK's O3 science run catalog, we use scaling arguments and assumptions on the source population models to estimate the run time required for LISA to accumulate a memory SNR of 5, using triggers from current and future ground-based detectors. Finally, we extend these calculations for using beyond LISA missions like ALIA, AMIGO, and Folkner to detect the gravitational memory effect. The results for LISA indicate a possible detection of the memory effect within the 10 year LISA mission lifetime and the corresponding results for beyond LISA missions are even more promising.

Detection of the gravitational memory effect in LISA using triggers from ground-based detectors

Vacuum conditions inside the LTP Gravitational Reference Sensor must comply with rather demanding requirements. The Optical Window (OW) is an interface which seals the vacuum enclosure and, at the same time, lets the laser beam go through for interferometric Metrology with the test masses. The OW is a plane-parallel plate clamped in a Titanium flange, and is considerably sensitive to thermal and stress fluctuations. It is critical for the required precision measurements, hence its temperature will be carefully monitored in flight. This paper reports on the results of a series of OW characterisation laboratory runs, intended to study its response to selected thermal signals, as well as their fit to numerical models, and the meaning of the latter. We find that a single pole ARMA transfer function provides a consistent approximation to the OW response to thermal excitations, and derive a relationship with the physical processes taking place in the OW. We also show how system noise reduction can be accomplished by means of that transfer function.

/pdf/thermal-diagnostic-of-the-optical-window-on-board-lisa-3fx0r66am0.pdf

Thermal diagnostic of the Optical Window on board LISA Pathfinder

Temperature fluctuations degrade the performance of different subsystems in the LISA mission. For instance, they can exert stray forces on the test masses and thus hamper the required drag-free accuracy. Also, the interferometric system performance depends on the stability of the temperature in the optical elements. Therefore, monitoring the temperature in specific points of the LISA subsystems is required. These measurements will be useful to identify the sources of excess noise caused by temperature fluctuations. The required temperature stability is still to be defined, but a figure around 10?K Hz?1/2 from 0.1 mHz to 0.1 Hz can be a good rough guess. The temperature measurement subsystem on board the LISA Pathfinder mission exhibits noise levels of 10?K Hz?1/2 for f >0.1 mHz. For LISA, based on the above hypothesis, the measurement system should overcome limitations related to the analog-to-digital conversion stage which degrades the performance of the measurement when temperature drifts. Investigations on the mitigation of such noise will be here presented.

ADC non-linear error corrections for low-noise temperature measurements in the LISA band

Tilt-to-length (TTL) noise from angular jitter in LISA is projected to be the dominant noise source in the milli-Hertz band unless corrected in post-processing. The correction is only possible after removing the overwhelming laser phase noise using time-delay interferometry (TDI). We present here a frequency domain model that describes the eﬀect of angular motion of all three spacecraft on the interferometric signals after propagating through TDI. We then apply a Fisher information matrix analysis to this model to calculate the minimum uncertainty with which TTL coupling coeﬃcients may be estimated. Furthermore, we show the impact of these uncertainties on the residual TTL noise in the gravitational wave readout channel, and compare it to the impact of the angular witness sensors’ readout noise. We show that the residual TTL noise post-subtraction in the TDI variables for a case using the LISA angular jitter requirement and integration time of one day is limited to the 8 pm/ √ Hz level by angular sensing noise. However, using a more realistic model for the angular jitter we ﬁnd that the TTL coupling uncertainties are 70 times larger, and the noise subtraction is limited by these uncertainties to the 14 pm/ √ Hz level.

J Sanjuán

Papers

Magnetic polarisation effects of temperature sensors and heaters in LISA Pathfinder

Detection of the gravitational memory effect in LISA using triggers from ground-based detectors

Thermal diagnostic of the Optical Window on board LISA Pathfinder

ADC non-linear error corrections for low-noise temperature measurements in the LISA band

Calculating the precision of tilt-to-length coupling estimation and noise subtraction in LISA using Fisher information