Ability of LIGO and LISA to probe the equation of state of the early Universe

Abstract

The expansion history of the Universe between the end of inflation and the onset of radiation-domination (RD) is currently unknown. If the equation of state during this period is stiffer than that of radiation, w > 1/3, the gravitational wave (GW) background from inflation acquires a blue-tilt d log ρ GW d log f = 2(w−1/3) (w+1/3) > 0 at frequencies f f RD corresponding to modes re-entering the horizon during the stiff-domination (SD), where f RD is the frequency today of the horizon scale at the SD-to-RD transition. We characterized in detail the transfer function of the GW energy density spectrum, considering both 'instant' and smooth modelings of the SD-to-RD transition. The shape of the spectrum is controlled by w, f RD , and H inf (the Hubble scale of inflation). We determined the parameter space compatible with a detection of this signal by LIGO and LISA, including possible changes in the number of relativistic degrees of freedom, and the presence of a tensor tilt. Consistency with upper bounds on stochastic GW backgrounds, however, rules out a significant fraction of the observable parameter space. We find that this renders the signal unobservable by Advanced LIGO, in all cases. The GW background remains detectable by LISA, though only in a small island of parameter space, corresponding to scenarios with an equation of state in the range 0.46 w 0.56 and a high inflationary scale H inf 10 13 GeV, but low reheating temperature 1 MeV T RD 150 MeV (equivalently, 10 −11 Hz f RD 3.6 · 10 −9 Hz). Implications for early Universe scenarios resting upon an SD epoch are briefly discussed.

Ultraviolet freeze-in and non-standard cosmologies

“…Finally, we highlight that direct searches for DM produced via UV freeze-in (with or without a boost factor) is likely challenging outside of special constructions or benign corners of parameter space, however primordial gravitational wave production from the era prior to radiation domination could provide a potential probe in the future [67][68][69][70][71].…”

Reconstructing the spectral shape of a stochastic gravitational wave background with LISA

“…Cosmological sources can provide SGWBs with power law spectra characterised by different slopes than the astrophysical ones: e.g. in the presence of a Kination dominated phase [46][47][48][49][50] the spectrum scales as ∝ f α , with 0.5 α 1, whereas a cosmic defect network gives a spectrum in the LISA band (for sufficiently large tension) scaling as a plateau ∝ f 0 [83,[86][87][88][89][90]145]. In certain inflationary scenarios, like in axion-inflation and its variants [12,15,[146][147][148][149][150][151], the spectrum of the GW signal may consist of a nearly flat part at low frequencies, followed by a smoothly growing part at high frequencies.…”

“…Furthermore, post-inflationary, early universe phenomena can also generate GWs with a large amplitude, e.g. a kination dominated phase [46][47][48][49][50], non-perturbative particle production phenomena [51][52][53][54][55][56][57][58][59][60][61][62], oscillon dynamics [63][64][65][66][67], strong first order phase transitions [68][69][70][71][72][73][74][75][76][77][78][79][80][81], or cosmic defect networks [82][83][84][85][86][87][88][89][90][91][92][93]. The resulting GW signal in such cases is given by the superposition of a very large number of uncorrelated and unresolved sources, and hence it is perceived by u...…”

Early cosmological evolution of primordial electromagnetic fields

“…The case ρ 1/4 inf = 1016 GeV (H inf ∼ 10 14 GeV) and s = 2 is within the region where backreaction and anisotropy constraints are satisfied[16] 16. An equation of state of w > 1/3 can also blue-tilt the primordial gravitational wave spectrum[45]. It would be interesting to study the possibility of probing w from a joint analysis of the magnetic fields and gravitational waves.…”