Primordial gravitational waves in nonstandard cosmologies

Assuming that inflation is followed by a phase where the energy density of the Universe is dominated by a component with a general equation of state, we evaluate the spectrum of primordial gravitational waves induced in the postinflationary Universe. We show that if the energy density of the Universe is dominated by a component $\varphi$ before big bang nucleosynthesis, its equation of state could be constrained by gravitational wave experiments depending on the ratio of energy densities of $\varphi$ and radiation and also the temperature at the end of the $\varphi$-dominated era. Also, we discuss the impact of scale dependence of tensor modes on the primordial gravitational wave spectrum during the $\varphi$ domination. These models are motivated by beyond Standard Model physics and scenarios for nonthermal production of dark matter in the early Universe. We also constrain the parameter space of the tensor spectral index and the tensor-to-scalar ratio, using the experimental limits from gravitational wave experiments.

Figure 1

The spectrum of inflationary GWs (${\mathrm{\Omega }}_{\mathrm{GW}}{h}^2$) as a function of the frequency $f$, for the standard cosmological scenario. Here we fix the inflationary scale as $V_{\inf }^{1/4}=1.5\times {10}^{16}\mathrm{GeV}$ and assume a primordial scale-invariant spectrum, i.e. $n_T=0$. We also show the temperature $T_{\mathrm{hc}}$ at which the corresponding mode reenters the horizon.

Figure 2

Example of the evolution of the energy densities ${\rho }_R$ and ${\rho }_{\varphi }$ as a function of the scale factor $a$, for ${\omega }_{\varphi }=0$ and $\xi ={10}^{-11}$ (upper panel), ${\omega }_{\varphi }=1/3$ and $\xi ={10}^{25}$ (central panel), and ${\omega }_{\varphi }=2/3$ and $\xi ={10}^{10}$ (lower panel). We have chosen $T_{\mathrm{dec}}=10\mathrm{MeV}$. These benchmark points are the same used in Fig. 3 and are shown in the upper left panel of Fig. 4. The vertical gray lines corresponding to $a=a_{\mathrm{eq}}$, $a_{\text{start}}$ and $a_{\mathrm{end}}$ are overlaid.

Figure 3

Spectra of inflationary GWs for ${\omega }_{\varphi }=0$ and $\xi ={10}^{-11}$ (upper panel), ${\omega }_{\varphi }=1/3$ and $\xi ={10}^{25}$ (central panel), and ${\omega }_{\varphi }=2/3$ and $\xi ={10}^{10}$ (lower panel). $T_{\mathrm{dec}}=10\mathrm{MeV}$ was also chosen. These benchmark points are the same used in Fig. 2 and are shown in the upper left panel of Fig. 4. The colored regions correspond to projected sensitivities for various gravitational wave observatories and to the BBN constraint described in the text.

Figure 4

Regions of the parameter space that could be tested by different observatories for a scale-invariant primordial spectrum ($n_T=0$), taking $V_{\inf }^{1/4}=1.5\times {10}^{16}$ (upper panels) and $1.5\times {10}^{15}\mathrm{GeV}$ (lower panels) and $T_{\mathrm{dec}}=10\mathrm{MeV}$ (left panels), 1 PeV (upper right panel) and 100 GeV (lower right panel). Three colored markers in the upper left panel are benchmark points for Figs. 2 and 3. The diagonal black dashed lines correspond to ${\xi }_{\min }$. The vertical red dotted lines correspond to ${\omega }_{\varphi }=1/3$.

Figure 5

Regions in the parameter space of the tensor-to-scalar ratio $r$ and the tensor tilt $n_T$ that can be probed by GW experiments in case of the standard radiation domination scenario. The regions above the colorful curves can be potentially excluded by different experiments. There are some comments in the right of plot in order, based on the minimum value of the tensor tilt that can be probed by each experiment. The dot-dashed purple line shows the upper bound on $r$ from CMB by the Planck satellite [109].

Figure 6

Regions of the parameter space that could be tested by different observatories assuming the consistency relation, Eq. (4.28), and $r=0.07$, for $T_{\mathrm{dec}}=10\mathrm{MeV}$ (left panel) and 1 PeV (right panel). The black dashed lines correspond to $\xi ={\xi }_{\min }$. The dotted red lines show the case ${\omega }_{\varphi }=1/3$.

Figure 7

Regions of the parameter space that could be tested by different observatories assuming $n_T=-0.3$ (left panel) and $n_T=0.3$ (right panel), for $T_{\mathrm{dec}}=10\mathrm{MeV}$. The black dashed lines correspond to $\xi ={\xi }_{\min }$. The red dotted lines show ${\omega }_{\varphi }=1/3$.