Black hole remnants in the early universe

We consider the production of primordial micro black holes (MBH) remnants in the early Universe. These objects induce the Universe to be in a matter-dominated era before the onset of inflation. Effects of such an epoch on the CMB power spectrum are discussed and computed both analytically and numerically. By comparison with the latest observational data from the WMAP collaboration, we find that our model appears to explain the quadrupole anomaly of the CMB power spectrum.

Figure 1

Diagram for $a(t)$ versus $t$, in a model assuming subsequent radiation and matter eras before inflation.

Figure 2

Nucleation rate, ${\Gamma }_{N,r}(\tau )$ over time $\tau$.

Figure 3

The cutoff as defined by the holographic principle at $\tau =993$: the curves touch, but the entropy of the black holes (full line) never exceeds the maximum entropy that can be held by the Hubble sphere (dashed line).

Figure 4

Ratio $R(\tau )$ of matter to radiation density in the early Universe, after the nucleation starts at $\tau =993$.

Figure 5

The mass density of the Universe as a function of time.

Figure 6

The collision rate of black holes (full line) in development with time, together with the Hubble rate (dashed line).

Figure 7

Black holes lifetime diagrams: the upper for an evaporating/absorbing black hole; the lower (dashed line) for an evaporating only black hole.

Figure 8

Diagram for $k$ versus $a$ (full line), in preinflation matter era.

Figure 9

Field $|\varphi (k)|$ versus $k$, in preinflation matter era (arbitrary units).

Figure 10

Primordial power spectrum $P(k)$ versus $k$, in preinflation matter era (arbitrary units).

Figure 11

Field $|\varphi (k)|$ versus $k$, in preinflation radiation era (arbitrary units).

Figure 12

Primordial power spectrum $P(k)$ versus $k$, in preinflation radiation era (arbitrary units).

Figure 13

Field $|\varphi (k)|$ versus $k$, for preinflation matter era (full/upper line), and radiation era (dashed/lower line).

Figure 14

Primordial power spectra $P(k)$ versus $k$, for preinflation matter (full/upper line) and radiation (dashed/lower line) eras.

Figure 15

The numerical solution for the primordial power spectrum (dashed line) and its fitting function (full line) in the preinflation matter era scenario.

Figure 16

The numerical solution for the primordial power spectrum (dashed line) and its fitting function (full line) in the preinflation radiation era scenario, with completely evaporating black holes (no GUP active).

Figure 17

The numerical solution for the primordial power spectrum (dashed line) and its fitting function (full line) in the preinflation radiation era scenario without black holes.

Figure 18

The binned CMB temperature anisotropy spectrum as measured by the WMAP satellite, in comparison with the standard inflationary scenario.

Figure 19

The CMB power spectrum for a preinflation matter era, for various cases of $\Delta N$. Overall view and zoom into the lower multipole region.

Figure 20

The CMB power spectrum for a preinflation radiation era, for various cases of $\Delta N$. Overall view and zoom into the lower multipole region.

Figure 21

The CMB power spectrum for a preinflation radiation era without any black holes, for various cases of $\Delta N$. Overall view and zoom into the lower multipole region.

Figure 22

The CMB power spectrum from the analytic solution of the approximated differential equation with matter-dominance and radiation-dominance, for various cases of $\Delta N$.

Figure 23

Comparing the CMB power spectrum for preinflation matter (full lines), radiation with black holes (dashed lines) and radiation without black holes (dashed-dotted lines) eras for $\Delta N=0.693147$, $\Delta N=2.07944$, $\Delta N=2.99573$, $\Delta N=3.58352$ and $\Delta N=4.09434$.

Figure 24

The distribution of ${\chi }^2$-values for a preinflation matter and radiation era, for various cases of $\Delta N$. Circles represent the matter model, whereas squares stand for the radiation model and triangles denote the case with radiation only. The horizontal line denotes the value of the SI scenario.