# The investigation of detectability of the relic gravitational waves based on the WMAP-9 and Planck

## TL;DR

This paper investigates the detectability of relic gravitational waves generated during the universe's inflation and reheating stages, analyzing their spectrum based on WMAP-9 and Planck data, and comparing with future detector sensitivities.

## Contribution

It provides an estimation of the allowed frequency range of relic gravitational waves considering reheating temperatures and observational constraints, enhancing detection prospects.

## Key findings

- Reheating temperature influences the gravitational wave spectrum.
- The spectrum's frequency range is constrained by WMAP-9 and Planck data.
- Future detectors may have improved chances to detect relic gravitational waves.

## Abstract

The generated relic gravitational waves were underwent several stages of evolution of the universe such as inflation and reheating. These stages were affected on the shape of spectrum of the waves. As well known, at the end of inflation, the scalar field $\phi$ oscillates quickly around some point where potential $V(\phi)=\lambda \phi^{n}$ has a minimum. The end of inflation stage played a crucial role on the further evolution stages of the universe because particles were created and collisions of the created particles were responsible for reheating the universe. There is a general range for the frequency of the spectrum $ \sim (0.3\times10^{-18}-0.6\times10^{10}$)Hz. It is shown that the reheating temperature can be affect on the frequency of the spectrum as well. There is constraint on the temperature from cosmological observations based on WMAP-9 and Planck. Therefore it is interesting to estimate allowed value of frequencies of the spectrum based on general range of reheating temperature like few MeV $\lesssim T_{rh}\lesssim10^{16}$ GeV, WMAP-9 and Planck data then compare the spectrum with sensitivity of future detectors such as LISA, BBO and ultimate-DECIGIO. The obtained results of this comparison give us some more chance for detection of the relic gravitational waves.