Search

Many early universe scenarios predict an enhancement of scalar perturbations at scales currently unconstrained by cosmological probes. These perturbations source gravitational waves (GWs) at second order in perturbation theory, leading to a scalar-induced gravitational wave (SIGW) background. The LISA detector, sensitive to mHz GWs, will be able to constrain curvature perturbations in a new window corresponding to scales $k \in [10^{10}, 10^{14}] \,{\rm Mpc}^{-1}$, difficult to probe otherwise. In this work, we forecast the capabilities of LISA to constrain the source of SIGWs using different approaches: i) agnostic, where the spectrum of curvature perturbations is binned in frequency space; ii) template-based, modeling the curvature power spectrum based on motivated classes of models; iii) ab initio, starting from first-principles model of inflation featuring an ultra-slow roll phase. We compare the strengths and weaknesses of each approach. We also discuss the impact on the SIGW spectrum of non-standard thermal histories affecting the kernels of SIGW emission and non-Gaussianity in the statistics of the curvature perturbations. Finally, we propose simple tests to assess whether the signal is compatible with the SIGW hypothesis. The pipeline used is built into the SIGWAY code., Comment: 95 pages, 31 figures

In the search for stochastic gravitational wave backgrounds (SGWB) of cosmological origin with LISA, it is crucial to account for realistic complications in the noise and astrophysical foreground modeling that may impact the signal reconstruction. To address these challenges, we updated the $\texttt{SGWBinner}$ code to incorporate both variable noise levels across LISA arms and more complex foreground spectral shapes. Our findings suggest that, while moderate variations of the noise amplitudes have a minimal impact, poor foreground modeling (i.e., templates requiring many free parameters) significantly degrades the reconstruction of cosmological signals. This underlines the importance of accurate modeling and subtraction of the astrophysical foregrounds to characterize possible cosmological components. To perform this more challenging analysis, we have integrated the $\texttt{JAX}$ framework, which significantly improves the computational efficiency of the code, in the $\texttt{SGWBinner}$ code, enabling faster Bayesian likelihood sampling and more effective exploration of complex SGWB signals., Comment: 30 pages, 9 figures

Variations in the instrumental noise of the Laser Interferometer Space Antenna (LISA) over time are expected as a result of e.g. scheduled satellite operations or unscheduled glitches. We demonstrate that these fluctuations can be leveraged to improve the sensitivity to stochastic gravitational wave backgrounds (SGWBs) compared to the stationary noise scenario. This requires optimal use of data segments with downward noise fluctuations, and thus a data analysis pipeline capable of analysing and combining shorter time segments of mission data. We propose that simulation based inference is well suited for this challenge. In an approximate, but state-of-the-art, modeling setup, we show by comparison with Fisher Information Matrix estimates that the optimal information gain can be achieved in practice., Comment: 12 pages, 5 figures. saqqara available at https://github.com/peregrine-gw/saqqara, GW_response available at https://github.com/Mauropieroni/GW_response

Pulsar Timing Array (PTA) observations have recently gathered substantial evidence for the existence of a gravitational wave background in the nHz frequency band. Searching for anisotropies in this signal is key to determining its origin, and in particular to distinguish possible astrophysical from cosmological sources. In this work, we assess the sensitivity of current and future pulsar timing arrays to such anisotropies using the full covariance matrix of pulsar timing delays. While current day pulsar timing arrays can only set mildly informative constraints on the dipole and quadrupole, we show that percent level accuracy for several low multipoles can be achieved in the near future. Moreover, we demonstrate that anisotropies in the gravitational wave background and the Hellings-Downs angular correlation, indicating the presence of GWs, are approximately uncorrelated, and can hence be reconstructed independently. These results can be reproduced with \href{https://github.com/Mauropieroni/fastPTA}{\texttt{fastPTA}}, a publicly available Python code to forecast the constraining power of PTA configurations., Comment: 20 pages, 10 figures, 3 appendices

Various scenarios of cosmic inflation enhance the amplitude of the stochastic gravitational wave background (SGWB) at frequencies detectable by the LISA detector. We develop tools for a template-based analysis of the SGWB and introduce a template databank to describe well-motivated signals from inflation, prototype their template-based searches, and forecast their reconstruction with LISA. Specifically, we classify seven templates based on their signal frequency shape, and we identify representative fundamental physics models leading to them. By running a template-based analysis, we forecast the accuracy with which LISA can reconstruct the template parameters of representative benchmark signals, with and without galactic and extragalactic foregrounds. We identify the parameter regions that can be probed by LISA within each template. Finally, we investigate how our signal reconstructions shed light on fundamental physics models of inflation: we discuss their impact for measurements of \emph{e.g.,} ~the couplings of inflationary axions to gauge fields; the graviton mass during inflation; the fluctuation seeds of primordial black holes; the consequences of excited states during inflation, and the presence of small-scale spectral features., Comment: 82 pages, 29 figures; v2 matches version published in JCAP

The existence of a primordial stochastic gravitational wave background (SGWB) is a common prediction in various models of the early Universe. Despite constraints at different frequency ranges and claims of detection in the nHz range by Pulsar Timing Arrays, the amplitude and spectral dependence of the SGWB in the mHz range remain largely unknown. Plausible models of early Universe Physics predict a wide range of SGWB amplitudes, from undetectable to exceeding the constraints from Big Bang Nucleosynthesis. This paper explores the potential impact of a prominent primordial SGWB on LISA's main scientific targets. Our main analyses focuses on Massive Black Hole Binaries (MBHBs). By employing publicly available MBHB population models and state-of-the-art LISA's forecasting pipeline, we analyze the effects of the SGWB on MBHB detections. We find that the decrease in the signal-to-noise ratio induced by a strong primordial GWB can significantly reduce the number of detectable events, compromise the precision of constraints, and even hinder sky localization for some events. We also examine the impact of the SGWB on Stellar Origin Black Hole Binaries (SOBHBs) and Galactic Binaries (GBs), which are fainter sources than MBHBs. Depending on the spectral properties of the SGWB, we conclude that these sources could be either marginally affected or rendered completely undetectable. This largely unexplored aspect raises critical questions about the potential challenges posed by a prominent SGWB to LISA's astrophysical objectives, including MBHBs, SOBHBs, and GBs., Comment: 15 pages, 7 figures; v2 matches version accepted by PRD

We initiate the LISA template databank for stochastic gravitational wave backgrounds sourced by cosmic strings. We include two templates, an analytical template, which enables more flexible searches, and a numerical template derived directly from large Nambu-Goto simulations of string networks. Using searches based on these templates, we forecast the parameter space within the reach of the experiment and the precision with which their parameters will be reconstructed, provided a signal is observed. The reconstruction permits probing the Hubble expansion and new relativistic DoF in the early universe. We quantify the impact that astrophysical foregrounds can have on these searches. Finally, we discuss the impact that these observations would have on our understanding of the fundamental models behind the string networks. Overall, we prove that LISA has great potential for probing cosmic string models and may reach tensions as low as $G\mu =10^{-16} - 10^{-17} $, which translates into energy scales of the order $10^{11}~\text{GeV}$., Comment: 59 pages, 15 figures

Pulsar Timing Array (PTA) observations hinted towards the existence of a stochastic gravitational wave background (SGWB) in the nHz frequency band. Still, the nature of the SGWB signal cannot be confidently inferred from current data, and the leading explanation invokes mergers of supermassive black holes. If confirmed, such discovery would not only represent a turning point in our understanding of astrophysics, but it may severely limit the capability of searching for additional cosmological sources in the nHz frequency range. In this work, we build a simple framework to forecast the sensitivity of future PTA configurations and assess the parameter estimation of SGWB, which could consist of several contributions. We release the python code fastPTA implementing this framework and ready to use., Comment: 16 pages, 9 figures

We develop a tool for the analysis of stochastic gravitational wave backgrounds from cosmological first-order phase transitions with LISA: we initiate a template databank for these signals, prototype their searches, and forecast their reconstruction. The templates encompass the gravitational wave signals sourced by bubble collisions, sound waves and turbulence. Accounting for Galactic and extra-Galactic foregrounds, we forecast the region of the parameter space that LISA will reconstruct with better than $\sim 10\,\%$ accuracy, if certain experimental and theoretical uncertainties are solved by the time LISA flies. We illustrate the accuracy with which LISA can reconstruct the parameters on a few benchmark signals, both in terms of the template parameters and the phase transition ones. To show the impact of the forecasts on physics beyond the Standard Model, we map the reconstructed benchmark measurements into the parameter spaces of the singlet extension of the Standard Model and of the classically conformal invariant $U(1)_{B-L}$ model., Comment: 54 pages, 18 figures; v2 matches version published in JCAP

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase., Comment: 155 pages, with executive summary and table of contents

We analyze the detection prospects for potential Primordial Black Hole Binary (PBHB) populations buried in the Stellar-Origin Black Hole Binary (SOBHB) population inferred by the LVK collaboration. We consider different PBHB population scenarios and several future Gravitational Wave (GW) detectors. To separate the PBHB component from the SOBHB one, we exploit the prediction that the PBHB merger rate does not decline as fast as the SOBHB one at high redshift. However, only a tiny fraction of PBHB events may be resolved individually, and the sub-threshold events may yield an undetectable Stochastic GW Background (SGWB). For this reason, we determine the statistical significance of the PBHB contributions in the number of resolvable events seen in future Earth-based detectors and the SGWB measured at LISA. We find that the synergy between these probes will consistently help assess whether or not a sizeable PBHB population is present., Comment: 31 pages, 8 figures

Gravitational Waves (GW) sourced by second-order primordial curvature fluctuations are among the favored models fitting the recent pulsar timing array (PTA) measurement of a stochastic GW background (SGWB). We study how spectral distortions (SDs) and anisotropies of the cosmic microwave background (CMB) can constrain such scalar fluctuations. Whereas COBE FIRAS data have no sufficient sensitivity to probe the PTA log-normal hypothesis, we show how future PIXIE-like experiments can detect the CMB SDs from the scalar-induced interpretation of the SGWB in PTA data. We finally show how the transformative synergy between PTA data and future CMB SD measurements is important for reconstructing primordial fluctuations at these small scales., Comment: 8 pages, 3 figures + supplemental materials. v2 matches version published by PRD

The next generation of space- and ground-based facilities promise to reveal an entirely new picture of the gravitational wave sky: thousands of galactic and extragalactic binary signals, as well as stochastic gravitational wave backgrounds (SGWBs) of unresolved astrophysical and possibly cosmological signals. These will need to be disentangled to achieve the scientific goals of experiments such as LISA, Einstein Telescope, or Cosmic Explorer. We focus on one particular aspect of this challenge: reconstructing an SGWB from (mock) LISA data. We demonstrate that simulation-based inference (SBI) - specifically truncated marginal neural ratio estimation (TMNRE) - is a promising avenue to overcome some of the technical difficulties and compromises necessary when applying more traditional methods such as Monte Carlo Markov Chains (MCMC). To highlight this, we show that we can reproduce results from traditional methods both for a template-based and agnostic search for an SGWB. Moreover, as a demonstration of the rich potential of SBI, we consider the injection of a population of low signal-to-noise ratio supermassive black hole transient signals into the data. TMNRE can implicitly marginalize over this complicated parameter space, enabling us to directly and accurately reconstruct the stochastic (and instrumental noise) contributions. We publicly release our TMNRE implementation in the form of the code saqqara., Comment: 6 pages, 2 figures, 1 table + supplemental material. Code: saqqara available at https://github.com/PEREGRINE-GW/saqqara. Matches published version

We discuss the interpretation of the detected signal by Pulsar Timing Array (PTA) observations as a gravitational wave background (GWB) of cosmological origin. We combine NANOGrav 15-years and EPTA-DR2new data sets and confront them against backgrounds from supermassive black hole binaries (SMBHBs), and cosmological signals from inflation, cosmic (super)strings, first-order phase transitions, Gaussian and non-Gaussian large scalar fluctuations, and audible axions. We find that scalar-induced, and to a lesser extent audible axion and cosmic superstring signals, provide a better fit than SMBHBs. These results depend, however, on modeling assumptions, so further data and analysis are needed to reach robust conclusions. Independently of the signal origin, the data strongly constrain the parameter space of cosmological signals, for example, setting an upper bound on primordial non-Gaussianity at PTA scales as $|f_{nl}| \lesssim 2.34$ at 95% CL., Comment: 5 pages, 2 figures, and Supplemental material. V3: The version published in PRL

We use the latest constraints on the population of stellar origin binary black holes (SOBBH) from LIGO/Virgo/KAGRA (LVK) observations, to estimate the stochastic gravitational wave background (SGWB) they generate in the frequency band of LISA. We account for the faint and distant binaries, which contribute the most to the SGWB, by extending the merger rate at high redshift assuming it tracks the star formation rate. We adopt different methods to compute the SGWB signal: an analytical evaluation, Monte Carlo sums over SOBBH population realisations, and a method that accounts for the role of the detector by simulating LISA data and iteratively removing resolvable signals until only the confusion noise is left, allowing for the extraction of both the expected SGWB and the number of resolvable SOBBHs. Since the latter are few for SNR thresholds larger than five, we confirm that the spectral shape of the SGWB in the LISA band follows the analytical prediction of a power law. We infer the probability distribution of the SGWB amplitude from the LVK GWTC-3 posterior of the binary population model; its interquartile range of $h^2\Omega_\mathrm{GW}(f=3\times10^{-3}\,\mathrm{Hz}) \in [5.65,\,11.5]\times10^{-13}$ is in agreement with most previous estimates. We perform a MC analysis to assess LISA's capability to detect and characterise this signal. Accounting for both the instrumental noise and the galactic binaries foreground, with four years of data, LISA will be able to detect the SOBBH SGWB with percent accuracy, narrowing down the uncertainty on the amplitude by one order of magnitude with respect to the range of possible amplitudes inferred from the population model. A measurement of this signal by LISA will help to break the degeneracy among some of the population parameters, and provide interesting constraints, in particular on the redshift evolution of the SOBBH merger rate., Comment: 39 pages, 15 figures. Prepared for submission to JCAP

We explore the impact of choosing different sets of Time-Delay Interferometry (TDI) variables for detecting and reconstructing Stochastic Gravitational Wave Background (SGWB) signals and estimating the instrumental noise in LISA. Most works in the literature build their data analysis pipelines relying on a particular set of TDI channels, the so-called AET variables, which are orthogonal under idealized conditions. By relaxing the assumption of a perfectly equilateral LISA configuration, we investigate to which degree these channels remain orthogonal and compare them to other TDI channels. We show that different sets of TDI variables are more robust under perturbations of the perfect equilateral configuration, better preserving their orthogonality and, thus, leading to a more accurate estimate of the instrumental noise. Moreover, we investigate the impact of considering the noise levels associated with each instrumental noise source to be independent of one another, generalizing the analysis from two to twelve noise parameters. We find that, in this scenario, the assumption of orthogonality is broken for all the TDI variables, leading to a misestimation of measurement error for some of the noise parameters. Remarkably, we find that for a flat power-law signal, the reconstruction of the signal parameters is nearly unaffected in these various configurations., Comment: 31 pages, 13 figures, and supplementary material

The Einstein Telescope (ET), the European project for a third-generation gravitational-wave detector, has a reference configuration based on a triangular shape consisting of three nested detectors with 10 km arms, where in each arm there is a `xylophone' configuration made of an interferometer tuned toward high frequencies, and an interferometer tuned toward low frequencies and working at cryogenic temperature. Here, we examine the scientific perspectives under possible variations of this reference design. We perform a detailed evaluation of the science case for a single triangular geometry observatory, and we compare it with the results obtained for a network of two L-shaped detectors (either parallel or misaligned) located in Europe, considering different choices of arm-length for both the triangle and the 2L geometries. We also study how the science output changes in the absence of the low-frequency instrument, both for the triangle and the 2L configurations. We examine a broad class of simple `metrics' that quantify the science output, related to compact binary coalescences, multi-messenger astronomy and stochastic backgrounds, and we then examine the impact of different detector designs on a more specific set of scientific objectives., Comment: 197 pages, 73 figures. v2: corrections in the part on the sensitivity to stochastic backgrounds. Accepted in JCAP

Effective field theories (EFT) of dark energy (DE) -- built to parameterise the properties of DE in an agnostic manner -- are severely constrained by measurements of the propagation speed of gravitational waves (GW). However, GW frequencies probed by ground-based interferometers lie around the typical strong coupling scale of the EFT, and it is likely that the effective description breaks down before even reaching that scale. We discuss how this leaves the possibility that an appropriate ultraviolet completion of DE scenarios, valid at scales beyond an EFT description, can avoid present constraints on the GW speed. Instead, additional constraints in the lower frequency LISA band would be harder to escape, since the energies involved are orders of magnitude lower. By implementing a method based on GW multiband detections, we show indeed that a single joint observation of a GW150914-like event by LISA and a terrestrial interferometer would allow one to constrain the speed of light and gravitons to match to within $10^{-15}$. Multiband GW observations can therefore firmly constrain scenarios based on the EFT of DE, in a robust and unambiguous way., Comment: 11 pages, 4 figures. Updated to match the version published in JCAP

Future gravitational wave detectors, such as the Laser Interferometer Space Antenna (\textit{LISA}), will be able to resolve a significant number of the ultra compact stellar-mass binaries in our own Galaxy and its neighborhood. These will be mostly double white dwarf (DWD) binaries, and their underlying population characteristics can be directly correlated to the different properties of the Galaxy. In particular, with \textit{LISA} we will be able to resolve $\sim\mathcal{O}(10^4)$ binaries, while the rest will generate a confusion foreground signal. Analogously to how the total electromagnetic radiation emitted by a galaxy can be related to the underlying total stellar mass, in this work we propose a framework to infer the same quantity by investigating the spectral shape and amplitude of the confusion foreground signal. For a fixed DWD evolution model, and thus a fixed binary fraction, we retrieve percentage-level relative errors on the total stellar mass, which improves for increasing values of the mass. At the same time, we find that variations in the Milky Way shape, at a fixed mass and at scale heights smaller than 500~pc, are not distinguishable based on the shape of stochastic signal alone. We perform this analysis on simulations of the LISA data, estimating the resolvable sources based on signal-to-noise criteria. Finally, we utilize the catalogue of resolvable sources to probe the characteristics of the underlying population of DWD binaries. We show that the DWD frequency, coalescence time and chirp mass (up to $<0.7\,$M$_\odot$) distributions can be reconstructed from \textit{LISA} data with no bias., Comment: 15 pages, 9 figures

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe.

We consider stellar-origin black hole binaries, which are among the main astrophysical sources for next generation gravitational wave (GW) detectors such as the Einstein Telescope (ET) and Cosmic Explorer (CE). Using population models calibrated with the most recent LIGO/Virgo results from O3b run, we show that ET and CE will be capable of detecting tens of thousands of such sources (and virtually all of those present in our past light cone up to $z\lesssim 0.7$ for ET and $z\lesssim 1$ for CE) with a signal-to-noise ratio up to several hundreds, irrespective of the detector design. When it comes to parameter estimation, we use a Fisher-matrix analysis to assess the impact of the design on the estimation of the intrinsic and extrinsic parameters. We find that the CE detector, consisting of two distinct $L-$shape interferometers, has better sky localization performance compared to ET in its triangular configuration. We also find that the network is typically capable of measuring the chirp mass, symmetric mass ratio and spins of the binary at order of $10^{-5}$, $10^{-4}$ and $10^{-4}$ fractional error respectively. While the fractional errors for the extrinsic parameters are of order $10^{-2}$ for the sky localization, luminosity distance and inclination., Comment: 17 pages+appendix, 12 figures; typos corrected; some results changed; updated to match published version

The propagation speed of gravitational waves, $c_T$, has been tightly constrained by the binary neutron star merger GW170817 and its electromagnetic counterpart, under the assumption of a frequency-independent $c_T$. Drawing upon arguments from Effective Field Theory and quantum gravity, we discuss the possibility that modifications of General Relativity allow for transient deviations of $c_T$ from the speed of light at frequencies well below the band of current ground-based detectors. We motivate two representative Ans\"atze for $c_T(f)$, and study their impact upon the gravitational waveforms of massive black hole binary mergers detectable by the LISA mission. We forecast the constraints on $c_T(f)$ obtainable from individual systems and a population of sources, from both inspiral and a full inspiral-merger-ringdown waveform. We show that LISA will enable us to place stringent independent bounds on departures from General Relativity in unexplored low-frequency regimes, even in the absence of an electromagnetic counterpart., Comment: 38+20 pages, 22 figures. V2: Analysis improved, to be published in JCAP

We discuss the possibility to measure particle couplings with stochastic gravitational wave backgrounds (SGWBs). Under certain circumstances a sequence of peaks of different amplitude and frequency -- a $stairway$ -- emerges in a SGWB spectrum, with each peak probing a different coupling. The detection of such signature opens the possibility to reconstruct couplings (spectroscopy) of particle species involved in high energy phenomena generating SGWBs. Stairway-like signatures may arise in causally produced backgrounds in the early Universe, e.g. from preheating or first order phase transitions. As a proof of principle we study a preheating scenario with an inflaton $\phi$ coupled to multiple $daughter$ fields $\lbrace \chi_j \rbrace$ with different coupling strengths. As a clear stairway signature is imprinted in the SGWB spectrum, we reconstruct the relevant couplings with various detectors., Comment: 4 pages, 3 figures and supplemental material

We investigate the sensitivity of the Laser Interferometer Space Antenna (LISA) to the anisotropies of the Stochastic Gravitational Wave Background (SGWB). We first discuss the main astrophysical and cosmological sources of SGWB which are characterized by anisotropies in the GW energy density, and we build a Signal-to-Noise estimator to quantify the sensitivity of LISA to different multipoles. We then perform a Fisher matrix analysis of the prospects of detectability of anisotropic features with LISA for individual multipoles, focusing on a SGWB with a power-law frequency profile. We compute the noise angular spectrum taking into account the specific scan strategy of the LISA detector. We analyze the case of the kinematic dipole and quadrupole generated by Doppler boosting an isotropic SGWB. We find that $\beta\, \Omega_{\rm GW}\sim 2\times 10^{-11}$ is required to observe a dipolar signal with LISA. The detector response to the quadrupole has a factor $\sim 10^3 \,\beta$ relative to that of the dipole. The characterization of the anisotropies, both from a theoretical perspective and from a map-making point of view, allows us to extract information that can be used to understand the origin of the SGWB, and to discriminate among distinct superimposed SGWB sources., Comment: 48 page + appendices, 13 figures

Oscillations in the frequency profile of the stochastic gravitational wave background are a characteristic prediction of small-scale features during inflation. In this paper we present a first investigation of the detection prospects of such oscillations with the upcoming space-based gravitational wave observatory LISA. As a proof of principle, we show for a selection of feature signals that the oscillations can be reconstructed with LISA, employing a method based on principal component analysis. We then perform a Fisher forecast for the parameters describing the oscillatory signal. For a sharp feature we distinguish between the contributions to the stochastic gravitational wave background induced during inflation and in the post-inflationary period, which peak at different frequencies. We find that for the latter case the amplitude of the oscillation is expected to be measurable with $< 10\%$ accuracy if the corresponding peak satisfies $h^2 \Omega_\textrm{GW} \gtrsim 10^{-12}$-$10^{-11}$, while for inflationary-era gravitational waves a detection of the oscillations requires a higher peak amplitude of $h^2 \Omega_\textrm{GW}$, as the oscillations only appear on the UV tail of the spectrum. For a resonant feature the detection prospects with LISA are maximised if the frequency of the oscillation falls into the range $\omega_\textrm{log} = 4$ to $10$. Our results confirm that oscillations in the frequency profile of the stochastic gravitational wave background are a worthwhile target for future detection efforts and offer a key for experimentally testing inflation at small scales., Comment: 28 pages, 15 figures

In this work we discuss the application of the Hamilton-Jacobi formalism on the scalar field implementation of Generalized Chaplygin Gas models. This corresponds to a Generalised Born-Infeld action for the scalar field, which in an initial fast-rolling phase mimics a matter-like behavior and in the final slow-rolling phase mimics a cosmological constant. In order to enrich the phenomenology of the model, we add an extra functional freedom, specified through a scalar potential for the field. Interestingly, we find that, due to the lifting induced by the non-standard kinetic term, an asymptotic de Sitter-like configuration can be obtained even for negative potentials. We show that at the background level, this model can easily mimic the {\Lambda}CDM model both with and without independent baryonic and radiation components., Comment: 20 pages, 6 figures, 1 appendix

The science objectives of the LISA mission have been defined under the implicit assumption of a 4 yr continuous data stream. Based on the performance of LISA Pathfinder, it is now expected that LISA will have a duty cycle of $\approx 0.75$, which would reduce the effective span of usable data to 3 yr. This paper reports the results of a study by the LISA Science Group, which was charged with assessing the additional science return of increasing the mission lifetime. We explore various observational scenarios to assess the impact of mission duration on the main science objectives of the mission. We find that the science investigations most affected by mission duration concern the search for seed black holes at cosmic dawn, as well as the study of stellar-origin black holes and of their formation channels via multi-band and multi-messenger observations. We conclude that an extension to 6 yr of mission operations is recommended., Comment: 50 pages, 19 figures, 5 tables. Matches version published in GERG

The Laser Interferometer Space Antenna (LISA) mission, scheduled for launch in the early 2030s, is a gravitational wave observatory in space designed to detect sources emitting in the milli-Hertz band. In contrast to the present ground based detectors, the LISA data are expected to be a signaldominated, with strong and weak gravitational wave signals overlapping in time and in frequency. Astrophysical population models predict a sufficient number of signals in the LISA band to blend together and form an irresolvable foreground noise. In this work, we present a generic method for characterizing the foreground signals originating from a given astrophysical population of coalescing compact binaries. Assuming idealized detector conditions and perfect data analysis technique capable of identifying and removing the bright sources, we apply an iterative procedure which allows us to predict the different levels of foreground noise.

Parity violation is a powerful observable to distinguish a cosmological background of Gravitational Waves (GWs) from an astrophysical one. Planar single GW interferometers, both on ground and in space, are unable to measure the net circular polarization of an isotropic Stochastic Gravitational Wave Background (SGWB). In this paper, we explore the possibility of detecting circular polarization of an isotropic SGWB by cross-correlating two space-based detectors planned to be launched around 2034: LISA and Taiji. We compute the response of such a network to chirality and we perform a Fisher forecast analysis on the $I$ and $V$ Stokes parameters for the SGWB. We find that a clear measurement of chirality can be claimed for a maximally chiral signal with $h^2 \, \Omega_{\rm GW} \simeq 10^{-12}$., Comment: 22 pages, 4 figures

We present a data analysis methodology for a model-independent reconstruction of the spectral shape of a stochastic gravitational wave background with LISA. We improve a previously proposed reconstruction algorithm that relied on a single Time-Delay-Interferometry (TDI) channel by including a complete set of TDI channels. As in the earlier work, we assume an idealized equilateral configuration. We test the improved algorithm with a number of case studies, including reconstruction in the presence of two different astrophysical foreground signals. We find that including additional channels helps in different ways: it reduces the uncertainties on the reconstruction; it makes the global likelihood maximization less prone to falling into local extrema; and it efficiently breaks degeneracies between the signal and the instrumental noise., Comment: 35 pages, 12 figures

Given the recent advances in gravitational-wave detection technologies, the detection and characterisation of gravitational-wave backgrounds (GWBs) with the Laser Interferometer Space Antenna (LISA) is a real possibility. To assess the abilities of the LISA satellite network to reconstruct anisotropies of different angular scales and in different directions on the sky, we develop a map-maker based on an optimal quadratic estimator. The resulting maps are maximum likelihood representations of the GWB intensity on the sky integrated over a broad range of frequencies. We test the algorithm by reconstructing known input maps with different input distributions and over different frequency ranges. We find that, in an optimal scenario of well understood noise and high frequency, high SNR signals, the maximum scales LISA may probe are $\ell_{\rm max} \lesssim 15$. The map-maker also allows to test the directional dependence of LISA noise, providing insight on the directional sky sensitivity we may expect., Comment: Corresponding author: Arianna I. Renzini, as a part of their PhD thesis. 13 pages, 9 figures

Metric perturbations affect the phase of gravitational waves as they propagate through the inhomogeneous universe. This effect causes Stochastic Gravitational Wave Backgrounds (SGWBs) to lose any phase coherence that may have been present at emission or horizon entry. We show that, for a standard cosmological model, this implies complete loss of coherence above frequencies $f \sim 10^{-12}$ Hz. The result is that any attempts to map SGWBs using phase-coherent methods have no foreseeable applications. Incoherent methods that solve directly for the intensity of the SGWBs are the only methods that can reconstruct the angular dependence of any SGWB., Comment: 6 pages, 3 figures. v2: typos corrected

Based on the rate of resolved stellar origin black hole and neutron star mergers measured by LIGO and Virgo, it is expected that these detectors will also observe an unresolved Stochastic Gravitational Wave Background (SGWB) by the time they reach design sensitivity. Since the same binaries observed by LIGO and Virgo pass through the LISA mHz frequency band at an earlier stage of their orbital evolution,it is foreseen that their SGWB will also be observable by LISA with Signal to Noise Ratio (SNR) $\sim 53$. Unlike the stochastic signal from Galactic white dwarf binaries, for which a subtraction is expected to be possible by exploiting its yearly modulation (induced by the motion of the LISA constellation), the background from unresolved stellar origin black hole and neutron star binaries acts as a foreground for other stochastic signals of cosmological or astrophysical origin, which may also be present in the LISA band. Here, we employ a principal component analysis to model and extract an additional hypothetical SGWB in the LISA band, without making any a priori assumptions on its spectral shape. At the same time, we account for the presence of the foreground from stellar origin black holes and neutron stars, as well as for possible uncertainties in the LISA noise calibration. We find that our technique leads to a linear problem and is therefore suitable for fast and reliable extraction of SGWBs with SNR up to ten times weaker than the LIGO/Virgo foreground, quite independently of their spectral shape., Comment: Matches published version and incorporates minor changes to be published as erratum. 18 pages, 4 figures, 2 appendixes

Parity violating interactions in the early Universe can source a stochastic gravitational wave background (SGWB) with a net circular polarization. In this paper, we study possible ways to search for circular polarization of the SGWB with interferometers. Planar detectors are unable to measure the net circular polarization of an isotropic SGWB. We discuss the possibility of using the dipolar anisotropy kinematically induced by the motion of the solar system with respect to the cosmic reference frame to measure the net circular polarization of the SGWB with planar detectors. We apply this approach to LISA, re-assessing previous analyses by means of a more detailed computation and using the most recent instrument specifications, and to the Einstein Telescope (ET), estimating for the first time its sensitivity to circular polarization. We find that both LISA and ET, despite operating at different frequencies, could detect net circular polarization with a signal-to-noise ratio of order one in a SGWB with amplitude $h^2 \Omega_\text{GW} \simeq 10^{-11}$. We also investigate the case of a network of ground based detectors. We present fully analytical, covariant formulas for the detector overlap functions in the presence of circular polarization. Our formulas do not rely on particular choices of reference frame, and can be applied to interferometers with arbitrary angles among their arms., Comment: 33 pages + appendices, 6 figures

We demonstrate that gravitational waves generated by efficient gauge preheating after axion inflation generically contribute significantly to the effective number of relativistic degrees of freedom $N_\mathrm{eff}$. We show that, with existing Planck limits, gravitational waves from preheating already place the strongest constraints on the inflaton's possible axial coupling to Abelian gauge fields. We demonstrate that gauge preheating can completely reheat the Universe regardless of the inflationary potential. Further, we quantify the variation of the efficiency of gravitational wave production from model to model and show that it is correlated with the tensor-to-scalar ratio. In particular, when combined with constraints on models whose tensor-to-scalar ratios would be detected by next-generation cosmic microwave background experiments, $r\gtrsim 10^{-3}$, constraints from $N_\mathrm{eff}$ will probe or rule out the entire coupling regime for which gauge preheating is efficient., Comment: v2: 6 pages, 2 figures; matches published version

We study gravitational wave production from gauge preheating in a variety of inflationary models, detailing its dependence on both the energy scale and the shape of the potential. We show that preheating into Abelian gauge fields generically leads to a large gravitational wave background that contributes significantly to the effective number of relativistic degrees of freedom in the early universe, $N_\mathrm{eff}$. We demonstrate that the efficiency of gravitational wave production is correlated with the tensor-to-scalar ratio, $r$. In particular, we show that efficient gauge preheating in models whose tensor-to-scalar ratio would be detected by next-generation cosmic microwave background experiments ($r \gtrsim 10^{-3}$) will be either detected through its contribution to $N_\mathrm{eff}$ or ruled out. Furthermore, we show that bounds on $N_\mathrm{eff}$ provide the most sensitive probe of the possible axial coupling of the inflaton to gauge fields regardless of the potential., Comment: v2: 23 pages, 10 figures; matches published version

Since the very beginning of astronomy the location of objects on the sky has been a fundamental observational quantity that has been taken for granted. While precise two dimensional positional information is easy to obtain for observations in the electromagnetic spectrum, the positional accuracy of current and near future gravitational wave detectors is limited to between tens and hundreds of square degrees, which makes it extremely challenging to identify the host galaxies of gravitational wave events or to confidently detect any electromagnetic counterparts. Gravitational wave observations provide information on source properties and distances that is complementary to the information in any associated electromagnetic emission and that is very hard to obtain in any other way. Observing systems with multiple messengers thus has scientific potential much greater than the sum of its parts. A gravitational wave detector with higher angular resolution would significantly increase the prospects for finding the hosts of gravitational wave sources and triggering a multi-messenger follow-up campaign. An observatory with arcminute precision or better could be realised within the Voyage 2050 programme by creating a large baseline interferometer array in space and would have transformative scientific potential. Precise positional information of standard sirens would enable precision measurements of cosmological parameters and offer new insights on structure formation; a high angular resolution gravitational wave observatory would allow the detection of a stochastic background and resolution of the anisotropies within it; it would also allow the study of accretion processes around black holes; and it would have tremendous potential for tests of modified gravity and the discovery of physics beyond the Standard Model., Comment: 26 pages, 2 figures. White paper submitted to ESA's Voyage 2050 call on behalf of the LISA Consortium 2050 Task Force

We present a set of tools to assess the capabilities of LISA to detect and reconstruct the spectral shape and amplitude of a stochastic gravitational wave background (SGWB). We first provide the LISA power-law sensitivity curve and binned power-law sensitivity curves, based on the latest updates on the LISA design. These curves are useful to make a qualitative assessment of the detection and reconstruction prospects of a SGWB. For a quantitative reconstruction of a SGWB with arbitrary power spectrum shape, we propose a novel data analysis technique: by means of an automatized adaptive procedure, we conveniently split the LISA sensitivity band into frequency bins, and fit the data inside each bin with a power law signal plus a model of the instrumental noise. We apply the procedure to SGWB signals with a variety of representative frequency profiles, and prove that LISA can reconstruct their spectral shape. Our procedure, implemented in the code SGWBinner, is suitable for homogeneous and isotropic SGWBs detectable at LISA, and it is also expected to work for other gravitational wave observatories., Comment: 40 pages, 22 figures

Classifying inflationary scenarios according to their scaling properties is a powerful way to connect theory with observations. A useful tool to make such a classification is the beta-function formalism. By describing inflation in terms of renormalization group equations, within this framework, it is possible to define universality classes, which can be considered as sets of theories that share a common scale invariant limit. In this paper we apply the formalism to define such classes of universality for models of inflation where the inflaton is coupled to gauge fields. We show that the formalism may consistently be extended to capture the peculiar features of these models such as statistical anisotropy. We also obtain some consistency conditions which serve as useful guidelines for model building., Comment: 29 pages, 1 figure, 2 appendices

The most up to date femto- and micro-lensing constraints indicate that primordial black holes of $\sim 10^{-16} M_\odot$ and $\sim 10^{-12} M_\odot$, respectively, may constitute a large fraction of the dark matter. We describe analytically and numerically the dynamics by which inflationary fluctuations featuring a time-varying propagation speed or an effective Planck mass can lead to abundant primordial black hole production. As an example, we provide an ad hoc DBI-like model. A very large primordial spectrum originating from a small speed of sound typically leads to strong coupling within the vanilla effective theory of inflationary perturbations. However, we point out that ghost inflation may be able to circumvent this problem. We consider as well black hole formation in solid inflation, for which, in addition to an analogous difficulty, we stress the importance of the reheating process. In addition, we review the basic formalism for the collapse of large radiation density fluctuations, emphasizing the relevance of an adequate choice of gauge invariant variables., Comment: 38 pages, matches JCAP version

The shift-symmetric coupling of a pseudo-scalar particle driving inflation to gauge fields provides a unique way of probing cosmic inflation. We show for an SU(2) gauge group how a classical isotropic background gauge field develops from the standard quantum mechanical vacuum in the far past. Over the course of inflation, the theory dynamically evolves from an approximately abelian regime into an inherently non-abelian regime, with distinct predictions for the scalar and tensor power spectra. The latter regime closely resembles a setup known as chromo-natural inflation, although our main focus here is on a new part of the parameter space which has received little attention so far. For single-field slow roll inflation models, large scales may exit the horizon in the abelian regime, ensuring agreement with the observations of the anisotropies in the cosmic microwave background, whereas smaller scales experience the non-abelian effects. This results in a strong enhancement of the stochastic gravitational wave background at small scales, e.g. at frequencies accessible with ground-based interferometers. For the scalar power spectrum, a similar enhancement arises due to non-linear contributions., Comment: 53 pages, 6 appendixes

We forecast the prospective of detection for a stochastic gravitational wave background sourced by cosmological first-order phase transitions. We focus on first-order phase transitions with negligible plasma effects, and consider the experimental infrastructures built by the end of the LISA mission. We make manifest the synergy among LISA, pulsar time array experiments, and ground-based interferometers. For phase transitions above the TeV scale or below the electroweak scale, LISA can detect the corresponding gravitational wave signal together with Einstein Telescope, SKA or even aLIGO-aVIRGO-KAGRA. For phase transitions at the electroweak scale, instead, LISA can be the only experiment observing the gravitational wave signal. In case of detection, by using a parameter reconstruction method that we anticipate in this work, we show that LISA on its own has the potential to determine when the phase transition occurs and, consequently, the energy scale above which the standard model of particle physics needs to be modified. The result may likely guide the collider community in the post-LHC era., Comment: 7 pages, 6 figures; v3: some clarifications, extra references, matches published version

The stochastic gravitational wave background (SGWB) contains a wealth of information on astrophysical and cosmological processes. A major challenge of upcoming years will be to extract the information contained in this background and to disentangle the contributions of different sources. In this paper we provide the formalism to extract, from the correlation of three signals in the Laser Interferometer Space Antenna (LISA), information about the tensor three-point function, which characterizes the non-Gaussian properties of the SGWB. This observable can be crucial to discriminate whether a SGWB has a primordial or astrophysical origin. Compared to the two-point function, the SGWB three-point function has a richer dependence on the gravitational wave momenta and chiralities. It can be used therefore as a powerful discriminator between different models. For the first time we provide the response functions of LISA to a general SGWB three-point function. As examples, we study in full detail the cases of an equilateral and squeezed SGWB bispectra, and provide the explicit form of the response functions, ready to be convoluted with any theoretical prediction of the bispectrum to obtain the observable signal. We further derive the optimal estimator to compute the signal-to-noise ratio. Our formalism covers general shapes of non-Gaussianity, and can be extended straightaway to other detector geometries. Finally, we provide a short overview of models of the early universe that can give rise to a non-Gaussian SGWB., Comment: Corrections added in the 3-point response function(s); Note added to discuss observability of the non-Gaussian signal; 33 pages + appendices, 5 Figures

Ideas borrowed from renormalization group are applied to warm inflation to characterize the inflationary epoch in terms of flows away from the de Sitter regime. In this framework different models of inflation fall into universality classes. Furthermore, for warm inflation this approach also helps to characterise when inflation can smoothly end into the radiation dominated regime. Warm inflation has a second functional dependence compared to cold inflation due to dissipation, yet despite this feature, it is shown that the universality classes defined for cold inflation can be consistently extended to warm inflation., Comment: 20 pages, 5 figures, 1 appendix

Protected by an approximate shift symmetry, axions are well motivated candidates for driving cosmic inflation. Their generic coupling to the Chern-Simons term of any gauge theory gives rise to a wide range of potentially observable signatures, including equilateral non-Gaussianites in the CMB, chiral gravitational waves in the range of direct gravitational wave detectors and primordial black holes (PBHs). In this paper we revisit these predictions for axion inflation models non-minimally coupled to gravity. Contrary to the case of minimally coupled models which typically predict scale-invariant mass distributions for the generated PBHs at small scales, we demonstrate how broadly peaked PBH spectra naturally arises in this setup. For specific parameter values, all of dark matter can be accounted for by PBHs., Comment: 33 pages plus appendices, 9 figures

In this contribution we discuss the possibility of generating an observable gravitational wave (GW) background by coupling a pseudo-scalar inflaton to some Abelian gauge fields. This analysis is performed by dividing inflationary models into universality classes. We find that of the most promising scenario is a Starobinsky-like model, which may lead to the generation of observational signatures both in upcoming CMB detectors as well as for direct GW detectors. The signal which can be produced in these models would both be observable in ground-based detectors, such as advanced LIGO, and in space-based detectors, such as LISA. The complementarity between the CMB and direct GW detection may be used to extract informations on the microphysics of inflation. Interestingly the mechanism discussed in this contribution may also be relevant for the generation of Primordial Black Holes (PBHs).

We discuss the cosmological evolution of a scalar field with non standard kinetic term in terms of a Renormalization Group Equation (RGE). In this framework inflation corresponds to the slow evolution in a neighborhood of a fixed point and universality classes for inflationary models naturally arise. Using some examples we show the application of the formalism. The predicted values for the speed of sound $c_s$ and for the amount of non-Gaussianities produced in these models are discussed. In particular, we show that it is possible to introduce models with $c_s^2 \neq 1$ that can be in agreement with present cosmological observations.

This work is focused on the study of early time cosmology and in particular on the study of inflation. After an introduction on the standard Big Bang theory, we discuss the physics of CMB and we explain how its observations can be used to set constraints on cosmological models. We introduce inflation and we carry out its simplest realization by presenting the observables and the experimental constraints that can be set on inflationary models. The possibility of observing primordial gravitational waves (GWs) produced during inflation is discussed. We present the reasons to define a classification of inflationary models and introduce the \beta-function formalism for inflation by explaining why in this framework we can naturally define a set of universality classes for inflationary models. Theoretical motivations to support the formulation of inflation in terms of this formalism are presented. Some generalized models of inflation are introduced and the extension of the \beta-function formalism for inflation to these models is discussed. Finally we focus on the study of models where the (pseudo-scalar) inflaton is coupled to some Abelian gauge fields that can be present during inflation. The analysis of the problem is carried out by using a characterization of inflationary models in terms of their asymptotic behavior. A wide set of theoretical aspects and of observational consequences is discussed., Comment: PhD thesis, 2016, Univ Paris Diderot

Current bounds from the polarization of the CMB predict the scale-invariant gravitational wave (GW) background of inflation to be out of reach for upcoming GW interferometers. This prospect dramatically changes if the inflaton is a pseudoscalar, in which case its generic coupling to any abelian gauge field provides a new source of GWs, directly related to the dynamics of inflation. This opens up new ways of probing the scalar potential responsible for cosmic inflation. Dividing inflation models into universality classes, we analyze the possible observational signatures. One of the most promising scenarios is Starobinsky inflation, which may lead to observational signatures both in direct GW detection as well as in upcoming CMB detectors. In this case, the complementarity between the CMB and direct GW detection, as well as the possibility of a multi-frequency analysis with upcoming ground and space based GW interferometers, may provide a first clue to the microphysics of inflation.

We discuss the introduction of a non minimal coupling between the inflaton and gravity in terms of the recently proposed $\beta$-function formalism for inflation\cite{Binetruy:2014zya}. Via a field redefinition we reduce to the case of minimally coupled theories. The universal attractor at strong coupling has a simple explanation in terms of the new field. Generalizations are discussed and the possibility of evading the universal attractor is shown.