Model independent results for the inflationary and reheating epochs. (arXiv:2003.09420v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+German_G/0/1/0/all/0/1">Gabriel German</a>
We address the problem of determining inflationary characteristics in a model
independent way and then study constraints for reheating. We start from a
recently proposed equation which allows to accurately calculate the value of
the inflaton at horizon crossing $phi_k$. We then use an equivalent form of
this equation to write a formula that relates the tensor-to-scalar index $ r $
to the number of e-folds during inflation $ N_k $, hence a general bound for $
N_k $ follows. In particular, at present $r < 0.063$ implies $N_k < 56.3$. We
also give an upper bound to the size of the universe, during the inflationary
epoch, that gave rise to the current observable universe. The reheating epoch
is discussed and a bound is given for the effective number of relativistic
degrees of freedom $ g_ {re} $ which translates into a bound for the reheat
temperature. From here bounds for the number of e-folds during reheating and
also during the radiation dominated epoch follow. A criteria to know whether
the constraint for the effective number of degrees of freedom exists is given
in terms of the ratio $ V_e / V_k $ where $V_e$ is the potential at the end of
inflation and $V_k$ at the horizon crossing scale $k$. Finally we study two
particular models: Starobinsky model, which was studied before and is mostly
used here for comparison, and a Mutated Hilltop Inflation (MHI) model. Tables
ref {table2} and ref {table3} show results for the two specific models of
inflation.
We address the problem of determining inflationary characteristics in a model
independent way and then study constraints for reheating. We start from a
recently proposed equation which allows to accurately calculate the value of
the inflaton at horizon crossing $phi_k$. We then use an equivalent form of
this equation to write a formula that relates the tensor-to-scalar index $ r $
to the number of e-folds during inflation $ N_k $, hence a general bound for $
N_k $ follows. In particular, at present $r < 0.063$ implies $N_k < 56.3$. We
also give an upper bound to the size of the universe, during the inflationary
epoch, that gave rise to the current observable universe. The reheating epoch
is discussed and a bound is given for the effective number of relativistic
degrees of freedom $ g_ {re} $ which translates into a bound for the reheat
temperature. From here bounds for the number of e-folds during reheating and
also during the radiation dominated epoch follow. A criteria to know whether
the constraint for the effective number of degrees of freedom exists is given
in terms of the ratio $ V_e / V_k $ where $V_e$ is the potential at the end of
inflation and $V_k$ at the horizon crossing scale $k$. Finally we study two
particular models: Starobinsky model, which was studied before and is mostly
used here for comparison, and a Mutated Hilltop Inflation (MHI) model. Tables
ref {table2} and ref {table3} show results for the two specific models of
inflation.
http://arxiv.org/icons/sfx.gif
