Abstract:We present a data analysis methodology for a model-independent reconstruction of the spectral shape of a stochastic gravitational wave background with LISA. We improve a previously proposed reconstruction algorithm that relied on a single Time-Delay-Interferometry (TDI) channel by including a complete set of TDI channels. As in the earlier work, we assume an idealized equilateral configuration. We test the improved algorithm with a number of case studies, including reconstruction in the presence of two differe… Show more
“…After this procedure, we coarse-grain the dataset following the procedure described in Sec. 3.1 of [20] to reduce the numerical complexity of the problem. In this section we will restrict our analysis to a single data stream, corresponding to the TDI X channel, and we will denote the data points as D k , where the index k runs over the reduced set of frequencies f k , and their weights 10 with n k .…”
Section: Principal Component Analysismentioning
confidence: 99%
“…Here we factored out the constant piece (1 + A 2 log C0) and absorbed it into h 2 ΩGW, resulting in this term appearing in the denominator of the amplitudes multiplying the oscillatory pieces. 9 We employ the same noise model as [20], we factor out the detector's response function and we convert to Ω units to directly work with the signals defined as in section 2. 10 Which simply correspond to the number of points we averaged over in the coarse-graining procedure.…”
Section: Principal Component Analysismentioning
confidence: 99%
“…Up to this point we have not specified any particular model for the signal and for the noise. Concerning noise we use the model described in [18], which is equivalent to the noise model of [20,37] with one caveat: we redefine the noise parameters in order to have a model which is linear in θ n and the new noise parameters are equal to one at face value. Concerning signal, in the rest of this section we assume the signal can be expanded as a sum over m normalized Gaussians δ σ (with zero mean and some σ) each centered around a certain pivot frequency f j with j ∈ 1, ..., m as:…”
Oscillations in the frequency profile of the stochastic gravitational wave background are a characteristic prediction of small-scale features during inflation. In this paper we present a first investigation of the detection prospects of such oscillations with the upcoming space-based gravitational wave observatory LISA. As a proof of principle, we show for a selection of feature signals that the oscillations can be reconstructed with LISA, employing a method based on principal component analysis. We then perform a Fisher forecast for the parameters describing the oscillatory signal. For a sharp feature we distinguish between the contributions to the stochastic gravitational wave background induced during inflation and in the post-inflationary period, which peak at different frequencies. We find that for the latter case the amplitude of the oscillation is expected to be measurable with < 10% accuracy if the corresponding peak satisfies h 2 Ω GW 10 −12 -10 −11 , while for inflationary-era gravitational waves a detection of the oscillations requires a higher peak amplitude of h 2 Ω GW , as the oscillations only appear on the UV tail of the spectrum. For a resonant feature the detection prospects with LISA are maximised if the frequency of the oscillation falls into the range ω log = 4 to 10. Our results confirm that oscillations in the frequency profile of the stochastic gravitational wave background are a worthwhile target for future detection efforts and offer a key for experimentally testing inflation at small scales.
“…After this procedure, we coarse-grain the dataset following the procedure described in Sec. 3.1 of [20] to reduce the numerical complexity of the problem. In this section we will restrict our analysis to a single data stream, corresponding to the TDI X channel, and we will denote the data points as D k , where the index k runs over the reduced set of frequencies f k , and their weights 10 with n k .…”
Section: Principal Component Analysismentioning
confidence: 99%
“…Here we factored out the constant piece (1 + A 2 log C0) and absorbed it into h 2 ΩGW, resulting in this term appearing in the denominator of the amplitudes multiplying the oscillatory pieces. 9 We employ the same noise model as [20], we factor out the detector's response function and we convert to Ω units to directly work with the signals defined as in section 2. 10 Which simply correspond to the number of points we averaged over in the coarse-graining procedure.…”
Section: Principal Component Analysismentioning
confidence: 99%
“…Up to this point we have not specified any particular model for the signal and for the noise. Concerning noise we use the model described in [18], which is equivalent to the noise model of [20,37] with one caveat: we redefine the noise parameters in order to have a model which is linear in θ n and the new noise parameters are equal to one at face value. Concerning signal, in the rest of this section we assume the signal can be expanded as a sum over m normalized Gaussians δ σ (with zero mean and some σ) each centered around a certain pivot frequency f j with j ∈ 1, ..., m as:…”
Oscillations in the frequency profile of the stochastic gravitational wave background are a characteristic prediction of small-scale features during inflation. In this paper we present a first investigation of the detection prospects of such oscillations with the upcoming space-based gravitational wave observatory LISA. As a proof of principle, we show for a selection of feature signals that the oscillations can be reconstructed with LISA, employing a method based on principal component analysis. We then perform a Fisher forecast for the parameters describing the oscillatory signal. For a sharp feature we distinguish between the contributions to the stochastic gravitational wave background induced during inflation and in the post-inflationary period, which peak at different frequencies. We find that for the latter case the amplitude of the oscillation is expected to be measurable with < 10% accuracy if the corresponding peak satisfies h 2 Ω GW 10 −12 -10 −11 , while for inflationary-era gravitational waves a detection of the oscillations requires a higher peak amplitude of h 2 Ω GW , as the oscillations only appear on the UV tail of the spectrum. For a resonant feature the detection prospects with LISA are maximised if the frequency of the oscillation falls into the range ω log = 4 to 10. Our results confirm that oscillations in the frequency profile of the stochastic gravitational wave background are a worthwhile target for future detection efforts and offer a key for experimentally testing inflation at small scales.
“…Besides being detected, these signals are also reasonably well reconstructed. We use the SGWBinner code [ 47 , 48 ] to test this feature. Fig.…”
Section: Characterization Of Stochastic Backgroundsmentioning
confidence: 99%
“…In each bin, the reconstruction follows the parametrization . At this stage of code development [ 48 ], we use a single TDI channel [ 47 ] as the consequent reconstruction improvements would rely on extra assumptions on the LISA noise. Figures 13 and 14 display the reconstruction perspective in the duration scenario T4C in the case of the SI7.1 and SI7.2 signals, respectively.…”
Section: Characterization Of Stochastic Backgroundsmentioning
The science objectives of the LISA mission have been defined under the implicit assumption of a 4-years continuous data stream. Based on the performance of LISA Pathfinder, it is now expected that LISA will have a duty cycle of $$\approx 0.75$$
≈
0.75
, which would reduce the effective span of usable data to 3 years. This paper reports the results of a study by the LISA Science Group, which was charged with assessing the additional science return of increasing the mission lifetime. We explore various observational scenarios to assess the impact of mission duration on the main science objectives of the mission. We find that the science investigations most affected by mission duration concern the search for seed black holes at cosmic dawn, as well as the study of stellar-origin black holes and of their formation channels via multi-band and multi-messenger observations. We conclude that an extension to 6 years of mission operations is recommended.
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