# Multiple lensing of the cosmic microwave background anisotropies

## Abstract

We study the gravitational lensing effect on the Cosmic Microwave Background (CMB) anisotropies performing a ray-tracing of the primordial CMB photons through intervening large-scale structures (LSS) distribution predicted by N-Body numerical simulations with a particular focus on the precise recovery of the lens-induced polarized counterpart of the source plane. We apply both a multiple plane ray-tracing and an effective deflection approach based on the Born approximation to deflect the CMB photons trajectories through the simulated lightcone. We discuss the results obtained with both these methods together with the impact of LSS non-linear evolution on the CMB temperature and polarization power spectra. We compare our results with semi-analytical approximations implemented in Boltzmann codes like, e.g., CAMB. We show that, with our current N-body setup, the predicted lensing power is recovered with good accuracy in a wide range of multipoles while excess power with respect to semi-analytic prescriptions is observed in the lensing potential on scales ℓ ∼> 3000. We quantify the impact of the numerical effects connected to the resolution in the N-Body simulation together with the resolution and band-limit chosen to synthesise the CMB source plane. We found these quantities to be particularly important for the simulation of B-mode polarization power spectrum.

- Authors:

- SISSA, Via Bonomea 256, 34136, Trieste (Italy)
- I.N.A.F, Osservatorio Astronomico di Brera, Via Bianchi 46, 23807, Merate (Italy)
- Dipartimento di Fisica e Astronomia, Alma Mater Studiorum Universita' di Bologna, viale Berti Pichat 6/2, I-40127, Bologna (Italy)

- Publication Date:

- OSTI Identifier:
- 22525920

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2015; Journal Issue: 03; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANISOTROPY; BORN APPROXIMATION; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; COSMIC PHOTONS; GRAVITATIONAL LENSES; LIGHT CONE; MULTIPOLES; POLARIZATION; RELICT RADIATION; RESOLUTION

### Citation Formats

```
Calabrese, M., Fabbian, G., Baccigalupi, C., Carbone, C., and Baldi, M., E-mail: mcalabre@sissa.it, E-mail: carmelita.carbone@brera.inaf.it, E-mail: gfabbian@sissa.it, E-mail: marco.baldi5@unibo.it, E-mail: bacci@sissa.it.
```*Multiple lensing of the cosmic microwave background anisotropies*. United States: N. p., 2015.
Web. doi:10.1088/1475-7516/2015/03/049.

```
Calabrese, M., Fabbian, G., Baccigalupi, C., Carbone, C., & Baldi, M., E-mail: mcalabre@sissa.it, E-mail: carmelita.carbone@brera.inaf.it, E-mail: gfabbian@sissa.it, E-mail: marco.baldi5@unibo.it, E-mail: bacci@sissa.it.
```*Multiple lensing of the cosmic microwave background anisotropies*. United States. doi:10.1088/1475-7516/2015/03/049.

```
Calabrese, M., Fabbian, G., Baccigalupi, C., Carbone, C., and Baldi, M., E-mail: mcalabre@sissa.it, E-mail: carmelita.carbone@brera.inaf.it, E-mail: gfabbian@sissa.it, E-mail: marco.baldi5@unibo.it, E-mail: bacci@sissa.it. Sun .
"Multiple lensing of the cosmic microwave background anisotropies". United States.
doi:10.1088/1475-7516/2015/03/049.
```

```
@article{osti_22525920,
```

title = {Multiple lensing of the cosmic microwave background anisotropies},

author = {Calabrese, M. and Fabbian, G. and Baccigalupi, C. and Carbone, C. and Baldi, M., E-mail: mcalabre@sissa.it, E-mail: carmelita.carbone@brera.inaf.it, E-mail: gfabbian@sissa.it, E-mail: marco.baldi5@unibo.it, E-mail: bacci@sissa.it},

abstractNote = {We study the gravitational lensing effect on the Cosmic Microwave Background (CMB) anisotropies performing a ray-tracing of the primordial CMB photons through intervening large-scale structures (LSS) distribution predicted by N-Body numerical simulations with a particular focus on the precise recovery of the lens-induced polarized counterpart of the source plane. We apply both a multiple plane ray-tracing and an effective deflection approach based on the Born approximation to deflect the CMB photons trajectories through the simulated lightcone. We discuss the results obtained with both these methods together with the impact of LSS non-linear evolution on the CMB temperature and polarization power spectra. We compare our results with semi-analytical approximations implemented in Boltzmann codes like, e.g., CAMB. We show that, with our current N-body setup, the predicted lensing power is recovered with good accuracy in a wide range of multipoles while excess power with respect to semi-analytic prescriptions is observed in the lensing potential on scales ℓ ∼> 3000. We quantify the impact of the numerical effects connected to the resolution in the N-Body simulation together with the resolution and band-limit chosen to synthesise the CMB source plane. We found these quantities to be particularly important for the simulation of B-mode polarization power spectrum.},

doi = {10.1088/1475-7516/2015/03/049},

journal = {Journal of Cosmology and Astroparticle Physics},

number = 03,

volume = 2015,

place = {United States},

year = {Sun Mar 01 00:00:00 EST 2015},

month = {Sun Mar 01 00:00:00 EST 2015}

}