Imprints of the QCD phase transition on the spectrum of gravitational waves

Abstract

We have investigated effects of the QCD phase transition on the relic GW spectrum applying several equations of state for the strongly interacting matter: Besides the bag model, which describes a first order transition, we use recent data from lattice calculations featuring a crossover. Finally, we include a short period of inflation during the transition which allows for a first order phase transition at finite baryon density. Our results show that the QCD transition imprints a step into the spectrum of GWs. Within the first two scenarios, entropy conservation leads to a step-size determined by the relativistic degrees of freedom before and after the transition. The inflation of the third scenario much stronger attenuates the high-frequency modes: An inflationary model being consistent with observation entails suppression of the spectral energy density by a factor of 10 −12 .Theories of inflation predict the existence of a background spectrum of gravitational waves (GWs) which has been created in the very early universe together with scalar perturbations of the energy density. Since then the GWs propagate freely through spacetime still retaining information about the conditions under which they originated. This is because their cross section is very small: Particles with larger cross section, such as neutrinos or photons, decouple much later and therefore carry no information about the universe at such early times and high energies. This advantage of GWs renders their direct detection impossible until today. However, observations of the binary pulsar B1913+16 (Hulse-Taylor pulsar) provide strong evidence for energy loss through emission of gravitational radiation [1].In this article we demonstrate that in spite of being decoupled, relic GWs can show imprints of subsequent cosmic events, e.g. phase transitions. We present the shape of the relic GW spectrum after different scenarios of the QCD phase transition. Before the transition, at about 200 MeV, the universe is filled with a fluid containing relativistic quarks (up, down and strange), gluons, leptons and photons. After the transition, quarks are confined into hadrons of which the pions are the only degrees of freedom which are still relativistic. From this reduction of degrees of freedom and the assumption of entropy conservation, the impact of the phase transition on the spectrum of GWs can be derived. Numerical calculations show that the shape of the spectrum after confinement and chiral symmetry breaking does not strongly depend on the order of the phase transition.However, there are scenarios for the cosmological QCD phase transition where entropy conservation is considerably violated and the gross features of the spectrum are not fixed by the estimates mentioned above. We will discuss a model which includes a short period with dominating vacuum energy density causing inflation. The melting of this energy is associated with a large entropy release. Within this model, the energy density in highfrequency GWs is much more diluted than within the scenarios ...

Cosmological and astrophysical probes of vacuum energy

“…The factor by which they are suppressed is approximately r ∼ (a 0 /a f ) 4 , where a 0 is the scale factor at the beginning of the inflationary regime, and a f is the scale factor when it ends. Modes which are outside the horizon during this short inflationary era are simply frozen, and remain immune to the rapidly growing scale factor [40].…”

Observational prospects for gravitational waves from hidden or dark chiral phase transitions

“…Strictly speaking, Eqs (37). to(39) are to be evaluated at the transition temperature -usually denoted as T * in the literature -rather than at the nucleation temperature Tn. However, as we will explicitly see in Section V, the chiral phase transitions under consideration exhibit virtually no supercooling, so that the thermal plasma is practically not reheated after the PT has completed and Tn T * holds to good approximation.…”

The quark gluon plasma equation of state and the expansion of the early Universe

“…Apart from these exotic phenomena, changing the equation of state we change the space-time evolution of the early Universe and this (specially when there is a phase transition) will change the emission of gravitational waves, as pointed out in [4], [5], [6] and very recently in [7]. In [8] the authors have considered different EOS for the QGP. They computed the energy-momentum tensor, performed a Fourier transform from the configuration to the momentum space and then, using a textbook formula from [9], computed the wave spectrum, i.e., the energy density radiated in gravitational waves as a function of the wave frequency.…”