We investigate constraints on the spectral index of primordial gravitational waves (GWs), paying particular attention to a blue-tilted spectrum. Such constraints can be used to test a certain class of models of the early Universe. We investigate obse
rvational bounds from LIGO+Virgo, pulsar timing and big bang nucleosynthesis, taking into account the suppression of the amplitude at high frequencies due to reheating after inflation and also late-time entropy production. Constraints on the spectral index are presented by changing values of parameters such as reheating temperatures and the amount of entropy produced at late time. We also consider constraints under the general modeling approach which can approximately describe various scenarios of the early Universe. We show that the constraints on the blue spectral tilt strongly depend on the underlying assumption and, in some cases, a highly blue-tilted spectrum can still be allowed.
We discuss how one can reconstruct the thermal history of the Universe by combining cosmic microwave background (CMB) measurements and gravitational wave (GW) direct detection experiments. Assuming various expansion eras to take place after the infla
tionary reheating and before Big-Bang Nucleosynthesis (BBN), we show how measurements of the GW spectrum can be used to break the degeneracies associated with CMB data, the latter being sensitive to the total amount of cosmic expansion only. In this context, we argue that the expected constraints from future CMB and GW experiments can probe a scenario in which there exists late-time entropy production in addition to the standard reheating. We show that, for some cases, combining data from future CMB and GW direct detection experiments allows the determination of the reheating temperature, the amount of entropy produced and the temperature at which the standard radiation era started.
The weak lensing (WL) distortions of distant galaxy images are sensitive to neutrino masses by probing the suppression effect on clustering strengths of total matter in large-scale structure. We use the latest measurement of WL correlations, the CFHT
LS data, to explore constraints on neutrino masses. We find that, while the WL data alone cannot place a stringent limit on neutrino masses due to parameter degeneracies, the constraint can be significantly improved when combined with other cosmological probes, the WMAP 5-year (WMAP5) data and the distance measurements of type-Ia supernovae (SNe) and baryon acoustic oscillations (BAO). The upper bounds on the sum of neutrino masses are m_tot = 1.1, 0.76 and 0.54 eV (95% CL) for WL+WMAP5, WMAP5+SNe+BAO, and WL+WMAP5+SNe+BAO, respectively, assuming a flat LCDM model with finite-mass neutrinos. In deriving these constraints, our analysis includes the non-Gaussian covariances of the WL correlation functions to properly take into account significant correlations between different angles.
