We examine which information on the early cosmological history can be extracted from the potential measurement by third-generation gravitational-wave observatories of a stochastic gravitational wave background (SGWB) produced by cosmic strings. We consider a variety of cosmological scenarios breaking the scale-invariant properties of the spectrum, such as early long matter or kination eras, short intermediate matter and inflation periods inside a radiation era, and their specific signatures on the SGWB. This requires to go beyond the usually-assumed scaling regime, to take into account the transient effects during the change of equation of state of the universe. We compute the time evolution of the string network parameters and thus the loop-production efficiency during the transient regime, and derive the corresponding shift in the turning-point frequency. We consider the impact of particle production on the gravitational-wave emission by loops. We estimate the reach of future interferometers LISA, BBO, DECIGO, ET and CE and radio telescope SKA to probe the new physics energy scale at which the universe has experienced changes in its expansion history. We find that a given interferometer may be sensitive to very different energy scales, depending on the nature and duration of the non-standard era, and the value of the string tension. It is fascinating that by exploiting the data from different GW observatories associated with distinct frequency bands, we may be able to reconstruct the full spectrum and therefore extract the values of fundamental physics parameters.

Kination denotes an era in the cosmological history corresponding to an equation of state ω = +1 such that the total energy density of the universe redshifts as the sixth inverse power of the scale factor. This arises if the universe is dominated by the kinetic energy of a scalar field. It has often been motivated in the literature as an era following inflation, taking place before the radiation era. In this paper, we review instead the possibility that kination is disconnected from primordial inflation and occurs much later, inside the Standard Model radiation era. We study the implications on all main sources of primordial gravitational waves. We show how this leads to very distinctive peaked spectra in the stochastic background of long-lasting cosmological sources of gravitational waves, namely the irreducible gravitational waves from inflation, and gravitational waves from cosmic strings, both local and global, with promising observational prospects. We present model-independent signatures and detectability predictions at LIGO, LISA, ET, CE, BBO, as a function of the energy scale and duration of the kination era. We then argue that such intermediate kination era is in fact symptomatic in a large class of axion models. We analyse in details the scalar field dynamics, the working conditions and constraints in the underlying models. We present the gravitational-wave predictions as a function of particle physics parameters. We derive the general relation between the gravitational-wave signal and the axion dark matter abundance as well as the baryon asymmetry. We investigate the predictions for the special case of the QCD axion. The key message is that gravitational-waves of primordial origin represent an alternative experimental probe of axion models.

Unstable heavy particles well above the TeV scale are unaccessible experimentally. So far, Big-Bang Nucleosynthesis (BBN) provides the strongest limits on their mass and lifetime, the latter being shorter than 0.1 second. We show how these constraints could be potentially tremendously improved by the next generation of Gravitational-Wave (GW) interferometers, extending to lifetimes as short as 10 −16 second. The key point is that these particles may have dominated the energy density of the universe and have triggered a period of matter domination at early times, until their decay before BBN. The resulting modified cosmological history compared to the usually-assumed single radiation era would imprint observable signatures in stochastic gravitationalwave backgrounds of primordial origin. In particular, we show how the detection of the GW spectrum produced by long-lasting sources such as cosmic strings would provide a unique probe of particle physics parameters. When applied to specific particle production mechanisms in the early universe, these GW spectra could be used to derive new constraints on many UV extensions of the Standard Model. We illustrate this on a few examples, such as supersymmetric models where the mass scale of scalar moduli and gravitino can be constrained up to 10 10 GeV. Further bounds can be obtained on the reheating temperature of models with only-gravitationally-interacting particles as well as on the kinetic mixing of heavy dark photons at the level of 10 −18 .

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.