Inflation with multi-vector hair: the fate of anisotropy

Abstract

We study inflation with multiple vector fields. In the presence of non-trivial couplings between the inflaton and the vector fields, it turns out that no-hair conjecture does not hold and vector hair appears. In the case of uniform couplings, nevertheless, we find that the universe approaches an isotropic final state after transient anisotropic inflationary phases. For general couplings, we numerically show that attractors are anisotropic inflation. Even in these cases, it turns out that the inflation always tends to minimize the anisotropy in the expansion of the universe.

Designing anisotropic inflation with form fields

“…It is worth investigating generation of magnetic fields in this context of cosmic democracy. In the present model, an isotropic inflation can be realized in spite of the presence of the gauge field and the two-form field because both tend to produce opposite anisotropy (This is similar to the multi-vector cases [11,14]. ).…”

“…In the case of the gauge field with this setup, we know there exists exact power-law solutions [5,11,12]. Hence, we expect new exact solutions can be found in the presence of the two-form field.…”

“…Given this configuration, in principle, the two-form field can take an arbitrary polarization. However, in the case of gauge fields, it has been shown that the fields tend to be orthogonal to make the expansion as isotropic as possible [11]. Thus, we assume the two-form field B µν has an orthogonal configuration 1 2 B µν dx µ ∧ dx ν = v B (t)dy ∧ dz to the gauge field.…”

Anisotropic constant-roll Inflation

“…This is because a gauge field and a two-form field produce opposite anisotropy. It is also interesting to apply our method to anisotropic inflation with multi-gauge field (two-form field) models [19,20]. We leave these issues for future work.…”

Isotropy theorem for cosmological Yang-Mills theories

“…The possibility that some of the unknown components of the universe at different epochs (inflaton field, dark matter or dark energy) could be described by means of homogeneous vector fields rather than scalar fields have conflicted traditionally with the stringent limits on isotropy imposed by CMB observations [1][2][3][4][5][6][7][8][9][10][11]. The only scenarios in which these limitations could be evaded are those in which either only the temporal components of the vector fields are present or, in the case in which spatial components are also evolving, if the vector configuration guarantees an isotropic energy-momentum tensor.…”