Cosmological attactors to general relativity and spontaneous scalarization with disformal coupling. (arXiv:1909.11756v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Silva_H/0/1/0/all/0/1">Hector O. Silva</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Minamitsuji_M/0/1/0/all/0/1">Masato Minamitsuji</a>
The canonical scalar-tensor theory model which exhibits spontaneous
scalarization in the strong-gravity regime of neutron stars has long been known
to predict a cosmological evolution for the scalar field which generically
results in severe violations of present-day Solar System constraints on
deviations from general relativity. We study if this tension can be alleviated
by generalizing this model to include a disformal coupling between the scalar
field $varphi$ and matter, where the Jordan frame metric ${tilde g}_{munu}$
is related to the Einstein frame one $g_{munu}$ by ${tilde
g}_{munu}=A(varphi)^2 (g_{munu}+Lambda, partial_mu varphi ,
partial_nuvarphi)$. We find that this broader theory admits a late-time
attractor mechanism towards general relativity. However, the existence of this
attractor requires a value of disformal scale of the order $Lambdagtrsim
H_0^{-2}$, where $H_0$ is the Hubble parameter of today, which is much larger
than the scale relevant for spontaneous scalarization of neutron stars $Lambda
sim R_s^{2}$ with $R_s (sim 10^{-22} H_0^{-1})$ being the typical radius of
these stars. The large values of $Lambda$ necessary for the attractor
mechanism (i) suppresses spontaneous scalarization altogether inside neutron
stars and (ii) induces ghost instabilities on scalar field fluctuations, thus
preventing a resolution of the tension. We argue that this is a general feature
of spontaneous scalarization models (either of neutron stars or black holes)
which involve dimensionful coupling parameters.
The canonical scalar-tensor theory model which exhibits spontaneous
scalarization in the strong-gravity regime of neutron stars has long been known
to predict a cosmological evolution for the scalar field which generically
results in severe violations of present-day Solar System constraints on
deviations from general relativity. We study if this tension can be alleviated
by generalizing this model to include a disformal coupling between the scalar
field $varphi$ and matter, where the Jordan frame metric ${tilde g}_{munu}$
is related to the Einstein frame one $g_{munu}$ by ${tilde
g}_{munu}=A(varphi)^2 (g_{munu}+Lambda, partial_mu varphi ,
partial_nuvarphi)$. We find that this broader theory admits a late-time
attractor mechanism towards general relativity. However, the existence of this
attractor requires a value of disformal scale of the order $Lambdagtrsim
H_0^{-2}$, where $H_0$ is the Hubble parameter of today, which is much larger
than the scale relevant for spontaneous scalarization of neutron stars $Lambda
sim R_s^{2}$ with $R_s (sim 10^{-22} H_0^{-1})$ being the typical radius of
these stars. The large values of $Lambda$ necessary for the attractor
mechanism (i) suppresses spontaneous scalarization altogether inside neutron
stars and (ii) induces ghost instabilities on scalar field fluctuations, thus
preventing a resolution of the tension. We argue that this is a general feature
of spontaneous scalarization models (either of neutron stars or black holes)
which involve dimensionful coupling parameters.
http://arxiv.org/icons/sfx.gif
