Figure 1: Cosmic Microwave Background from ESA and the Planck Collaboration (2013).

Figure 1: Cosmic Microwave Background from ESA and the Planck Collaboration (2013).

CMB Circular Polarization and Cosmic Birefringence: arXiv:1803.04505

Figure 2: Polarization of the CMB. ESA and the Planck Collaboration (2015)

Figure 2: Polarization of the CMB from ESA and the Planck Collaboration (2015)

One of my current research projects consists on exploring different conventional sources of Circular Polarization (CP) in the Cosmic Microwave Background (CMB). The CMB is known to be linearly polarized  (at a level of ∼10%) due to anisotropic Thomson scattering. Therefore, any CP will come from propagation effects.

The most convenient mechanism (after the last scattering surface) to produce CP out of Linear Polarization (LP) is to use birefringence. Basically, a birefringent material has different indices of refraction, which then produce a phase shift  in the LP that generates CP. Hence we are looking at propagation effects that can produce a small degree of circular polarization in a CMB photon. Note that since the Universe is isotropic and homogeneous any birefringence must come from perturbations (either matter or radiation).

The sources of cosmic birefringence that we have studied in our work are: spin-polarized hydrogen atoms (both at recombination and at the Cosmic Dawn), photon-photon scattering (non-linear response of the vacuum by creation and annihilation of pairs), static non-linear hyperpolarizability of hydrogen (non-linear response of bounded electrons, e.g. hydrogen atom potential is not a harmonic oscillator), and plasma delay (non-linear response of free electrons). These sources are conventional in the sense that no physics outside the Standard model is introduced.

The strongest source of cosmic birefringence we studied is the photon-photon scattering, which imprints a CP in the CMB at a level of ∼10^{-14} K (the LP of the CMB is ∼10^{-6} K). Even though different results float around in the literature for this particular effect, we made sure of explaining all apparent contradictions.

Figure 3: Power spectrum of the circular polarization of the CMB due to photon-photon scattering.

The level of CP in the CMB generated by conventional sources of cosmic birefringence is small both in comparison to relevant foregrounds (e.g. galactic synchrotron emission…) and current and near-term experimental sensitivities.

Binary Neutron Stars Mergers:

Figure 4: Neutron star collision. (Credit: NASA/Swift/Dana Berry)

Since the discovery of gravitational waves sourced by binary black holes mergers from the LIGO collaboration, the interest in other sources of gravitational waves has increased exponentially. Furthermore, LIGO has recently discovered it’s first neutron star binary merger, opening the window to a lot of new interesting physics and new opportunities.

However, there are several unknowns (for example the equation of state) when dealing with neutron stars mergers that might play an important role in the inspiral, merging and ringdown phases. One of such unknowns corresponds to a possible instability pointed out by Nevin Weinberg et al. Basically, this instability arises from the tidal interaction with the companion neutron star. The main consequence of this instability would be the additional flow (or loss) of energy put into the orbit, which then will provoke a tiny phase shift per cycle in the inspiral. However, in contrast to black hole mergers the number of cycles for neutron star mergers can be large (around 3000), thus a tiny phase shift can propagate into an order unity effect.

This phase shift will modify the parameters obtained by LIGO because their templates would be slightly wrong for this kind of system. Also, in the most extreme scenario it could made LIGO unable to detect a whole class of binary neutron star mergers, the ones with a strong instability (kind of like a Reynolds number, systems above that critical number will present important instabilities).

One of our current projects consists on exploring and understanding of the effects and causes of this instability from a more theoretical perspective, instead of simulations.

More coming soon.

Exact and Approximate Solutions of the Einstein Equations: arXiv:1405.1776, 1609.00102

During my undergraduate program I worked on this topic with Prof. Frutos and Prof. Bonatti in University of Costa Rica. The motivation for this topic consists on the problem regarding the interior matching of the Kerr metric.

The Kerr metric represents a massive spinning body (such as any physical star), the static limit is the expected Schwarzschild metric. However, both of these metrics are exterior metrics.   There has not been an appropriate interior matching for the Kerr metric. One possible solution is to consider a metric that is more general than Kerr by modifying the geometry, i.e. more degrees of freedom to play with. However, does not matter what you do the new metric must be able to reproduce the Kerr metric at a certain limit.

For more information see the list of publications.


A list of publications can be seen below.


  • Montero-Camacho, P. and Hirata, C. M. (2018) Exploring circular polarization in the CMB due to conventional sources of cosmic birefringence. ArXiv preprint:1803.04505.
  • Frutos-Alfaro, F., Montero-Camacho, P., Araya, M. and Bonatti-Gonzalez, J. (2015) Approximate Metric for a Rotating Deformed Mass. International Journal of Astronomy and Astrophysics, 5, 1-10. doi:10.4236/ijaa.2015.51001.
  • Montero-Camacho, P., Frutos-Alfaro, F., Gutierrez-Chaves, C. and Cordero-Garcia, I. (2015) Slowly Rotating Curzon-Chazy Metric. Revista de Matematica: Teoria y Aplicaciones22 (2): 265-274.