Toy model based analysis on the effect of the Lee-Wick partners in the evolution of the early universe

Abstract

In the present article the thermodynamic results of the Lee-Wick partner infested universe have been applied in a toy model where there is one Lee-Wick partner to each of the standard model particles, and moreover, the longitudinal degrees of freedom of the massive partners of the standard massless gauge bosons are neglected at high temperatures. For practical purposes, the chiral fermionic sector of Lee-Wick theories requires two Lee-Wick partners per fermion, which opens up the possibility for a negative energy density of the early universe. A toy Lee-Wick model with one fermionic partner relaxes such oddities and hence is easy to deal with. In a similar way, the longitudinal degrees of freedom of the massive gauge boson partners also have the potential to yield negative energy densities, and thus those will be neglected in a toy model study. In such a toy model one can analytically calculate the time-temperature relation in the very early radiation dominated universe which shows interesting new physics. The article also tries to point out how a Lee-Wick particle dominated early cosmology transforms into the standard cosmological model. Based on the results of this toy model analysis a brief discussion is presented on the more realistic model, which can accommodate two Lee-Wick partners for each standard fermionic field and the longitudinal degree of freedom of partners of the gauge fields. It has been shown that such a universe is mostly very difficult to attain, but there are certain conditions where one can indeed think of such a universe which can evolve into the standard cosmological universe in a short time duration.

Lee-Wick standard model at finite temperature

“…To make this cancellation explicit in the LWSM, consider For the case σ = −1, we find that the free energy density is positive, which implies that the pressure, energy density, and entropy densities are negative. This result has been obtained previously in the context of toy LW theories [4,11], and its interesting implications have been studied in the context of early universe cosmology [37,38].…”

“…References [37,38] studied the effect of LW theories on very early universe cosmology using the case that we call σ = −1. They find that the unusual thermodynamic properties of LW theories can lead to novel features, such as bouncing cosmologies and mini-reheating events when LW particles decouple.…”

Lee-Wick radiation induced bouncing universe models

“…[19] that in the fermionic sector each chiral fermion requires two Lee-Wick partners to eliminate the higher derivative terms in an initial higher derivative Lagrangian to construct a Lee-Wick theory. Such discrepancies also arise in the bosonic sector when one considers massive Lee-Wick partners (with three degrees of freedom) of massless gauge bosons (with two longitudinal degrees of freedom) [20]. Both these cases lead to unacceptable scenarios with negative energy density.…”

“…It is shown in Ref. [20] that considering both the fermionic and bosonic sector together one still can come up with a scenario where the total energy density, pressure and entropy density can become positive. In a realistic scenario, where each fermion is accompanied by two Lee-Wick partners and the extra degrees of freedom of the massive Lee-Wick partners of each massless gauge boson are taken into account, the total energy density of the realistic Lee-Wick plasma can be written as [20] …”

“…[18] that in such kind of a Lee-Wick partner infested radiation dominated universe the time-temperature relation in standard cosmology changes and the universe may go through out-ofequilibrium processes when some of the Lee-Wick partners become nonrelativistic. It was noticed that these kinds of cosmologies can produce negative energy densities and pressure when one includes chiral fermions and massless gauge bosons [19,20]. This particular point turned out to be a serious drawback for these models.…”