Sachs-Wolfe Effect
The Sachs-Wolfe effect (after Rainer K. Sachs and Arthur M. Wolfe , who discovered it in 1967) explains fluctuations in the redshift of the photons of the cosmic background radiation . In addition to the silk damping and acoustic oscillations of the plasma in the early universe, it is one of three effects with which it is possible in astrophysics to calculate states in the early universe .
It makes it possible to read from the fluctuations in the redshift of the cosmic background radiation how the structure of matter in space must have been at the time of recombination , around 400,000 years after the Big Bang . In particular, the curvature parameter k of space-time can be determined in this way.
Sachs-Wolfe equation
The Sachs-Wolfe equation for determining the fluctuations in the temperature of the cosmic background radiation is:
Here designated
- the compliant time
- the position vector
- the direction unit vector
- the direction-independent monopole of cosmic background radiation, which corresponds to the isotropic average temperature.
Exact equation
The Sachs-Wolfe equation results from the linearized Boltzmann equation for small perturbations as follows:
It denotes:
- the visibility function ; the probability that a photon of the cosmic background radiation observed today was last scattered at a certain time ,
- the optical thickness ,
- Disturbances of the FLRW metric in the time-like / space-like component; in the Newtonian limit case can be understood as a disturbance of the gravitational potential ,
- the speed of baryonic matter and
- a canceled quantity is the partial derivative according to the conforming time
Approximate equation
Assuming that no reionization has taken place, which can visibility function can be approximated by a delta function at the time of decoupling of photons ( decoupling )
This leads directly to the fact that the exponential of the optical depth can be written as a Heaviside function :
This makes the approximated Sachs-Wolfe equation to
Explanation
Non-integrated Sachs-Wolfe effect
The non-integrated Sachs-Wolfe effect is due to the fact that at the time of the decoupling of the photons from the matter in the universe there were areas in some places whose gravitational potential deviated from the isotropic background. Because of these potential differences, the photons that come from an area with a higher / lower gravitational potential experience a relative gravitational red / blue shift . This effect is reflected in the equation by the difference .
The non-integrated Sachs-Wolfe effect is the most important term in the Sachs-Wolfe equation.
Integrated Sachs-Wolfe effect
During the propagation of the photons through the universe, they continue to encounter the anisotropies of baryonic matter. In the case of a static universe, due to the conservation of energy, when leaving an anisotropy , the photons would again take up the same energy that they gave off when they entered the anisotropy. However, since the universe has expanded in time, the gravitational potential flattens out as the photon passes through the anisotropy. This is the integrated Sachs-Wolfe effect represented by the term .
In the course of the development of the universe, further anisotropies arise through structure formation; however, these are negligible.
Other components of the Sachs-Wolfe equation
The other two terms of the Sachs-Wolfe equation can be classically explained without cosmological effects or the general theory of relativity :
- denotes the intrinsic temperature fluctuations of the photons at the time of decoupling.
- is the classic Doppler effect from the relative movement of the baryon photon fluid to the observer.
Measurements
With WMAP it was possible in 2001 to obtain strong indications of the existence of the hypothetical dark energy through the Sachs-Wolfe effect . This energy, still unknown in nature, is responsible for the expansion movement of the universe and makes up about 70% of its energy. The curvature parameter k of spacetime resulted from the measurements at k = 0, which means that the universe is a flat manifold . However, since a perfect measurement is impossible, the universe can be very slightly curved and this can be in the range of the measurement error .
The ESA Planck telescope was launched in May 2009, providing a ten times more accurate resolution of the background radiation and enabling better investigations.
literature
- RK Sachs, AM Wolfe: Perturbations of a Cosmological Model and Angular Variations of the Microwave Background . In: The Astrophysical Journal . tape 147 , 1967, ISSN 0004-637X , pp. 73 , doi : 10.1086 / 148982 .
Videos
- What is the Sachs-Wolfe Effect? from the alpha-Centauri television series(approx. 15 minutes). First broadcast on Nov 23, 2005.